Araştırma Makalesi
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Yıl 2019, Cilt: 1 Sayı: 1, 30 - 47, 09.04.2019

Öz

Kaynakça

  • [1] Bernstein. S, Sur les equations du calcul des variations, Ann. Sci. Ecole Norm. Sup. 29 (1912),431-485.
  • [2] Bebernes, J., Lacey, A. A., Global existence and nite-time blow-up for a class of nonlocalparabolic problems, Adv. Dierential Equations 2(6) (1997), 927-953.
  • [3] Barutello, V., Secchi, S., Serra, E, A note on the radial solutions for the supercritical Hnonequation. J. Math. Anal. Appl. 341(1), 720-728 (2008).
  • [4] Brezis, H., Nirenberg, L, Positive solutions of nonlinear elliptic equations involving criticalSobolev exponents. Commun. Pure Appl. Math. 36(4), 437-477, (1983)
  • [5] Bandle. C, Co man. C. V. and Marcus. M, Nonlinear elliptic problems in the annulus, J.Di erential Equations 69 (1978), 322-345.
  • [6] Bonheure. D and Serra. E, Multiple positive radial solutions on annulus for nonlinear Neu-mann problems with large growth, Nonlinear Di er. Equ. Appl. 18 (2011), 217-235.
  • [7] Butler. D, Ko. E, Kyuong. E and Shivaji. R, Positive radial solutions for elliptic equations onexterior domains with nonlinear boundary conditions, Communications on Pure and AppliedAnalysis Volume 13, Number 6, (2014), 2713-27631.
  • [8] N. Bouteraa and S. Benaicha, Triple positive solutions of higher-order nonlinear boundary value problems, Journal of Computer Science and Computational Mathematics, Volume 7, Issue 2, June 2017, 25-31.
  • [9] N. Bouteraa and S. Benaicha, H. Djourdem and M. Elarbi Benatia, Positive solutions for fourth-order two-point boundary value problem with a parameter, Romanian Journal of Mathematic and Computer Science. 2018, Vol 8, Issue 1 (2018), p 17-30.
  • [10] N. Bouteraa, S. Benaicha , H. Djourdem and N. Benatia, Positive solutions of nonlinear fourth-order two-point boundary value problem with a parameter, Romanian Journal of Mathematics and Computer science, 2018, Volume 8, Issue 1, p.17-30.
  • [11] Bouteraa. N and Benaicha. N, Existence of solutions for third-order three-point boundaryvalue problem, Mathematica. 60 (83), No 1, 2018, pp. 12-22.
  • [12] Chipot. M, Rodriguez. J. F, On a class of nonlocal nonlinear elliptic problems, Math. Modl.Nume. Anal. 26, 3 (1992), 447-468.
  • [13] Chipot. M, Roy. P, Existence results for some elliptic functional equations, (2013).[14] Cianciaruso. F, Infante. G and Pietramala, Solutions of perturbed Hammerstein integralequations with applications, Nonl. Anal. Real World Appl. 33 (2017), 317-347.
  • [15] Deimling. K, Nonlinear Functional Analysis, Springer, Berlin, Germany, 1985.[16] Egorov. Y and Kondratiev. V, On Spectral Theory of Elliptic Operators, Birkhauser, Basel,Boston, Berlin, 1996.
  • [17] Granas. A, Gunther. R and Lee. J, On a theorem of S. Bernstein, Pacic J. Math. 74 (1978),67-82.
  • [18] Guo. D, Nonlinear Functional Analysis, Shandong Science and Technologie, Jinan, China,1985.[19] Guo. D, Lakshmikantham. V, Nonlinear Problems in Abstract Cones, Acad. Press, Inc.,Boston, MA, 1988.
  • [20] Grossi. M, Asymptotic behaviour of the Kazdan{Warner solution in the annulus. J. Di .Eqns. 223, 96{111 (2006).
  • [21] Han. G and Wang. J, Multiple positive radial solutions of elliptic equations in an exteriordomain, Monatshefte fur Mathematik, vol. 148, no. 3, pp. 217-228, 2006.
  • [22] Hakimi. S, Zertiti. A, Nonexistence of radial positive solutions for a nonpositone problem,Elec. J. Differ. Equ. 26 (2011), 1-7.
  • [23] Infante. G and Pietramala. P, Nonzero radial solutions for a class of elliptic systems withnonlocal BCs on annular domains, NODEA Nonlinear Di erential Equations Appl. 22 (2015),979-1003.
  • [24] Krasnosel'skii, M, Positive Solutions of Operator Equations, P. Noordho Ltd., Groningen,1964.
  • [25] Krasnoselskii. M. A and Zabreiko. P. P, Geometrical Methods of Nonlinear Analysis, Springer,New York, NY, USA, 1984.
  • [26] Krzywicki. A, Nadzieja. T, Nonlocal elliptic problems. Evolution equations: existence, regu-larity and singularities, Banach Center Publ. 52 (2000), Polish Acad. Sci., Warsaw, 147-152.
  • [27] Lions. P. L, On the existence of positive solutions of semilinear elliptic equations, SIAM Rev.24 (1982), 441-467.
  • [28] Ma. R, Existence of positive radial solutions for elliptic systems, J. Math. Anal. Appl. 201(1996), 375-386.
  • [29] Marcos do O. J, Lorca. S, Sanchez. J and Ubilla. P, Positive solutions for some nonlocal andnonvariational elliptic systems, Comp. Variab. Ellip. Equ. (2015), 18 pages.
  • [30] Ni. W. M, Nussbaum. R. D, Uniqueness and nonuniqueness for positive radial solutions ofu + f (u; r) = 0. Commun. Pure Appl. Math. 38(1), 67{108 (1985)
  • [31] Ockedon. J, Howison. S, A. Lacey and A. Movchan, Applied Partial Di erential Equations,Oxford University Press, 2003.
  • [32] Ovono. A. A, Rougirel, Elliptic equations with di usion parameterized by the range of non-local interactions, Annali di Mathematica. 009-0104-y (2009).
  • [33] Protter. M. H and Weinberger. H. F, Maximum principles in di erential equations, PrinticeHall, New-York, NY, USA, 1967.
  • [34] Stanczy. R, Positive solutions for superlinear elliptic equations, Journal of Applied Analysis,vol. 283, pp. 159{166, 2003.
  • [35] Sfecci. A, Nonresonance conditions for radial solutions of nonlinear Neumann elliptic problemson annuli, Rend. Istit. Mat. Univ. Trieste Volume 46 (2014), 255-270.
  • [36] Wang. H, On the existence of positive radial solutions for semilinear elliptic equations in theannulus, J. Di erential Equations 109 (1994), 1-8.
  • [37] Wu. Y and Han. G, On positive radial solutions for a class of elliptic equations, The Scienti cWorld Journal. Volume 2014, 11 pages.

On the Existence and Multiplicity of Positive Radial Solutions for Nonlinear Elliptic Equation on Bounded Annular Domains via Fixed Point Index

Yıl 2019, Cilt: 1 Sayı: 1, 30 - 47, 09.04.2019

Öz

In this paper, we study the existence and multiplicity of positive radial solutions for a class of local elliptic boundary value problem defined on bounded annular domains. The existence and multiplicity of positive radial solutions are obtained by means of fixed point index theory. We include an example to illustrate our results.

Kaynakça

  • [1] Bernstein. S, Sur les equations du calcul des variations, Ann. Sci. Ecole Norm. Sup. 29 (1912),431-485.
  • [2] Bebernes, J., Lacey, A. A., Global existence and nite-time blow-up for a class of nonlocalparabolic problems, Adv. Dierential Equations 2(6) (1997), 927-953.
  • [3] Barutello, V., Secchi, S., Serra, E, A note on the radial solutions for the supercritical Hnonequation. J. Math. Anal. Appl. 341(1), 720-728 (2008).
  • [4] Brezis, H., Nirenberg, L, Positive solutions of nonlinear elliptic equations involving criticalSobolev exponents. Commun. Pure Appl. Math. 36(4), 437-477, (1983)
  • [5] Bandle. C, Co man. C. V. and Marcus. M, Nonlinear elliptic problems in the annulus, J.Di erential Equations 69 (1978), 322-345.
  • [6] Bonheure. D and Serra. E, Multiple positive radial solutions on annulus for nonlinear Neu-mann problems with large growth, Nonlinear Di er. Equ. Appl. 18 (2011), 217-235.
  • [7] Butler. D, Ko. E, Kyuong. E and Shivaji. R, Positive radial solutions for elliptic equations onexterior domains with nonlinear boundary conditions, Communications on Pure and AppliedAnalysis Volume 13, Number 6, (2014), 2713-27631.
  • [8] N. Bouteraa and S. Benaicha, Triple positive solutions of higher-order nonlinear boundary value problems, Journal of Computer Science and Computational Mathematics, Volume 7, Issue 2, June 2017, 25-31.
  • [9] N. Bouteraa and S. Benaicha, H. Djourdem and M. Elarbi Benatia, Positive solutions for fourth-order two-point boundary value problem with a parameter, Romanian Journal of Mathematic and Computer Science. 2018, Vol 8, Issue 1 (2018), p 17-30.
  • [10] N. Bouteraa, S. Benaicha , H. Djourdem and N. Benatia, Positive solutions of nonlinear fourth-order two-point boundary value problem with a parameter, Romanian Journal of Mathematics and Computer science, 2018, Volume 8, Issue 1, p.17-30.
  • [11] Bouteraa. N and Benaicha. N, Existence of solutions for third-order three-point boundaryvalue problem, Mathematica. 60 (83), No 1, 2018, pp. 12-22.
  • [12] Chipot. M, Rodriguez. J. F, On a class of nonlocal nonlinear elliptic problems, Math. Modl.Nume. Anal. 26, 3 (1992), 447-468.
  • [13] Chipot. M, Roy. P, Existence results for some elliptic functional equations, (2013).[14] Cianciaruso. F, Infante. G and Pietramala, Solutions of perturbed Hammerstein integralequations with applications, Nonl. Anal. Real World Appl. 33 (2017), 317-347.
  • [15] Deimling. K, Nonlinear Functional Analysis, Springer, Berlin, Germany, 1985.[16] Egorov. Y and Kondratiev. V, On Spectral Theory of Elliptic Operators, Birkhauser, Basel,Boston, Berlin, 1996.
  • [17] Granas. A, Gunther. R and Lee. J, On a theorem of S. Bernstein, Pacic J. Math. 74 (1978),67-82.
  • [18] Guo. D, Nonlinear Functional Analysis, Shandong Science and Technologie, Jinan, China,1985.[19] Guo. D, Lakshmikantham. V, Nonlinear Problems in Abstract Cones, Acad. Press, Inc.,Boston, MA, 1988.
  • [20] Grossi. M, Asymptotic behaviour of the Kazdan{Warner solution in the annulus. J. Di .Eqns. 223, 96{111 (2006).
  • [21] Han. G and Wang. J, Multiple positive radial solutions of elliptic equations in an exteriordomain, Monatshefte fur Mathematik, vol. 148, no. 3, pp. 217-228, 2006.
  • [22] Hakimi. S, Zertiti. A, Nonexistence of radial positive solutions for a nonpositone problem,Elec. J. Differ. Equ. 26 (2011), 1-7.
  • [23] Infante. G and Pietramala. P, Nonzero radial solutions for a class of elliptic systems withnonlocal BCs on annular domains, NODEA Nonlinear Di erential Equations Appl. 22 (2015),979-1003.
  • [24] Krasnosel'skii, M, Positive Solutions of Operator Equations, P. Noordho Ltd., Groningen,1964.
  • [25] Krasnoselskii. M. A and Zabreiko. P. P, Geometrical Methods of Nonlinear Analysis, Springer,New York, NY, USA, 1984.
  • [26] Krzywicki. A, Nadzieja. T, Nonlocal elliptic problems. Evolution equations: existence, regu-larity and singularities, Banach Center Publ. 52 (2000), Polish Acad. Sci., Warsaw, 147-152.
  • [27] Lions. P. L, On the existence of positive solutions of semilinear elliptic equations, SIAM Rev.24 (1982), 441-467.
  • [28] Ma. R, Existence of positive radial solutions for elliptic systems, J. Math. Anal. Appl. 201(1996), 375-386.
  • [29] Marcos do O. J, Lorca. S, Sanchez. J and Ubilla. P, Positive solutions for some nonlocal andnonvariational elliptic systems, Comp. Variab. Ellip. Equ. (2015), 18 pages.
  • [30] Ni. W. M, Nussbaum. R. D, Uniqueness and nonuniqueness for positive radial solutions ofu + f (u; r) = 0. Commun. Pure Appl. Math. 38(1), 67{108 (1985)
  • [31] Ockedon. J, Howison. S, A. Lacey and A. Movchan, Applied Partial Di erential Equations,Oxford University Press, 2003.
  • [32] Ovono. A. A, Rougirel, Elliptic equations with di usion parameterized by the range of non-local interactions, Annali di Mathematica. 009-0104-y (2009).
  • [33] Protter. M. H and Weinberger. H. F, Maximum principles in di erential equations, PrinticeHall, New-York, NY, USA, 1967.
  • [34] Stanczy. R, Positive solutions for superlinear elliptic equations, Journal of Applied Analysis,vol. 283, pp. 159{166, 2003.
  • [35] Sfecci. A, Nonresonance conditions for radial solutions of nonlinear Neumann elliptic problemson annuli, Rend. Istit. Mat. Univ. Trieste Volume 46 (2014), 255-270.
  • [36] Wang. H, On the existence of positive radial solutions for semilinear elliptic equations in theannulus, J. Di erential Equations 109 (1994), 1-8.
  • [37] Wu. Y and Han. G, On positive radial solutions for a class of elliptic equations, The Scienti cWorld Journal. Volume 2014, 11 pages.
Toplam 34 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Bouteraa Noureddine

Slimane Benaicha Bu kişi benim

Habib Djourdem Bu kişi benim

Yayımlanma Tarihi 9 Nisan 2019
Kabul Tarihi 29 Mart 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 1 Sayı: 1

Kaynak Göster

APA Noureddine, B., Benaicha, S., & Djourdem, H. (2019). On the Existence and Multiplicity of Positive Radial Solutions for Nonlinear Elliptic Equation on Bounded Annular Domains via Fixed Point Index. Maltepe Journal of Mathematics, 1(1), 30-47.
AMA Noureddine B, Benaicha S, Djourdem H. On the Existence and Multiplicity of Positive Radial Solutions for Nonlinear Elliptic Equation on Bounded Annular Domains via Fixed Point Index. Maltepe Journal of Mathematics. Nisan 2019;1(1):30-47.
Chicago Noureddine, Bouteraa, Slimane Benaicha, ve Habib Djourdem. “On the Existence and Multiplicity of Positive Radial Solutions for Nonlinear Elliptic Equation on Bounded Annular Domains via Fixed Point Index”. Maltepe Journal of Mathematics 1, sy. 1 (Nisan 2019): 30-47.
EndNote Noureddine B, Benaicha S, Djourdem H (01 Nisan 2019) On the Existence and Multiplicity of Positive Radial Solutions for Nonlinear Elliptic Equation on Bounded Annular Domains via Fixed Point Index. Maltepe Journal of Mathematics 1 1 30–47.
IEEE B. Noureddine, S. Benaicha, ve H. Djourdem, “On the Existence and Multiplicity of Positive Radial Solutions for Nonlinear Elliptic Equation on Bounded Annular Domains via Fixed Point Index”, Maltepe Journal of Mathematics, c. 1, sy. 1, ss. 30–47, 2019.
ISNAD Noureddine, Bouteraa vd. “On the Existence and Multiplicity of Positive Radial Solutions for Nonlinear Elliptic Equation on Bounded Annular Domains via Fixed Point Index”. Maltepe Journal of Mathematics 1/1 (Nisan 2019), 30-47.
JAMA Noureddine B, Benaicha S, Djourdem H. On the Existence and Multiplicity of Positive Radial Solutions for Nonlinear Elliptic Equation on Bounded Annular Domains via Fixed Point Index. Maltepe Journal of Mathematics. 2019;1:30–47.
MLA Noureddine, Bouteraa vd. “On the Existence and Multiplicity of Positive Radial Solutions for Nonlinear Elliptic Equation on Bounded Annular Domains via Fixed Point Index”. Maltepe Journal of Mathematics, c. 1, sy. 1, 2019, ss. 30-47.
Vancouver Noureddine B, Benaicha S, Djourdem H. On the Existence and Multiplicity of Positive Radial Solutions for Nonlinear Elliptic Equation on Bounded Annular Domains via Fixed Point Index. Maltepe Journal of Mathematics. 2019;1(1):30-47.

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