Derleme
BibTex RIS Kaynak Göster
Yıl 2019, Cilt: 2 Sayı: 1, 25 - 35, 30.04.2019

Öz

Kaynakça

  • [1] J. Berkovits, C. Fabry, Semilinear problems with a non-symmetric linear part having an infinite dimensional kernel, Port. Math. 61 (2004) 439–459.
  • [2] J. Berkovits, C. Fabry, An extension of the topological degree in Hilbert space, Abstr. Appl. Anal. 2005:6 (2005) 581–597.
  • [3] J. Berkovits, V. Mustonen, An extension of Leray-Schauder degree and applications to nonlinear wave equations, Differ. Integral Equ. 3 (1990) 945–963.
  • [4] J. Berkovits, M. Tienari, Topological degree theory for some classes of multis with applications to hyperbolic and elliptic problems involving discontinuous nonlinearities, Dyn. Syst. Appl. 5 (1996) 1–18.
  • [5] H. Brézis, L. Nirenberg, Characterizations of the ranges of some nonlinear operators and applications to boundary value problems, Ann. Sc. Norm. Super. Pisa, Cl. Sci. 5 (1978) 225–326.
  • [6] H. Brézis, L. Nirenberg, Forced vibrations for a nonlinear wave equation, Commun. Pure Appl. Math. 31 (1978) 1–30. [7] J.B. Conway, A Course in Functional Analysis, 2nd ed., Springer, New York, 1990.
  • [8] C. Fabry, Inequalities verified by asymmetric nonlinear operators, Nonlinear Anal. 33 (1998) 121–137
  • [9] C. Fabry, A. Fonda, F. Munyamarere, Semilinear equations at resonance with non-symmetric linear part, J. Math. Anal. Appl. 180 (1993) 189–206.
  • [10] A. Fonda, Existence and uniqueness of solutions for semilinear equations involving anti-selfadjoint operators, Port. Math. 71 (2014) 183–192.
  • [11] H. Hofer, A multiplicity result for a class of nonlinear problems with applications to a nonlinear wave equation, Nonlinear Anal. 5 (1981) 1–11.
  • [12] I.-S. Kim, S.-J. Hong, Semilinear systems with a multi-valued nonlinear term, Open Math. 15 (2017) 628–644.
  • [13] T.-W. Ma, Topological degrees of set-valued compact fields in locally convex spaces, Dissertationes Math. Rozprawy Mat. 92 (1972), 43 pp.
  • [14] J. Mawhin, Nonlinear functional analysis and periodic solutions of semilinear wave equations, In: Laksmikantham, V(ed.) Nonlinear Phenomena in Mathematical Sciences, pp. 671–681, Academic Press, New York, 1982.
  • [15] J. Mawhin, M. Willem, Operators of monotone type and alternative problems with infinite dimensional kernel, Recent Advances in Differential Equations (Trieste 1978), pp. 295–307, Academic Press, New York, 1981.
  • [16] E. Zeidler, Nonlinear Functional Analysis and its Applications. I, Springer, New York, 1985.
  • [17] E. Zeidler, Nonlinear Functional Analysis and its Applications II/B, Springer, New York, 1990

Semilinear problems involving nonlinear operators of monotone type

Yıl 2019, Cilt: 2 Sayı: 1, 25 - 35, 30.04.2019

Öz

This is a survey article on semilinear problems with a non-symmetric linear part and a nonlinear part of monotone type in real Hilbert spaces.

We study the solvability of semilinear inclusions in the nonresonance and resonance cases. Semilinear systems consisting of semilinear equations of

different types are discussed.

Kaynakça

  • [1] J. Berkovits, C. Fabry, Semilinear problems with a non-symmetric linear part having an infinite dimensional kernel, Port. Math. 61 (2004) 439–459.
  • [2] J. Berkovits, C. Fabry, An extension of the topological degree in Hilbert space, Abstr. Appl. Anal. 2005:6 (2005) 581–597.
  • [3] J. Berkovits, V. Mustonen, An extension of Leray-Schauder degree and applications to nonlinear wave equations, Differ. Integral Equ. 3 (1990) 945–963.
  • [4] J. Berkovits, M. Tienari, Topological degree theory for some classes of multis with applications to hyperbolic and elliptic problems involving discontinuous nonlinearities, Dyn. Syst. Appl. 5 (1996) 1–18.
  • [5] H. Brézis, L. Nirenberg, Characterizations of the ranges of some nonlinear operators and applications to boundary value problems, Ann. Sc. Norm. Super. Pisa, Cl. Sci. 5 (1978) 225–326.
  • [6] H. Brézis, L. Nirenberg, Forced vibrations for a nonlinear wave equation, Commun. Pure Appl. Math. 31 (1978) 1–30. [7] J.B. Conway, A Course in Functional Analysis, 2nd ed., Springer, New York, 1990.
  • [8] C. Fabry, Inequalities verified by asymmetric nonlinear operators, Nonlinear Anal. 33 (1998) 121–137
  • [9] C. Fabry, A. Fonda, F. Munyamarere, Semilinear equations at resonance with non-symmetric linear part, J. Math. Anal. Appl. 180 (1993) 189–206.
  • [10] A. Fonda, Existence and uniqueness of solutions for semilinear equations involving anti-selfadjoint operators, Port. Math. 71 (2014) 183–192.
  • [11] H. Hofer, A multiplicity result for a class of nonlinear problems with applications to a nonlinear wave equation, Nonlinear Anal. 5 (1981) 1–11.
  • [12] I.-S. Kim, S.-J. Hong, Semilinear systems with a multi-valued nonlinear term, Open Math. 15 (2017) 628–644.
  • [13] T.-W. Ma, Topological degrees of set-valued compact fields in locally convex spaces, Dissertationes Math. Rozprawy Mat. 92 (1972), 43 pp.
  • [14] J. Mawhin, Nonlinear functional analysis and periodic solutions of semilinear wave equations, In: Laksmikantham, V(ed.) Nonlinear Phenomena in Mathematical Sciences, pp. 671–681, Academic Press, New York, 1982.
  • [15] J. Mawhin, M. Willem, Operators of monotone type and alternative problems with infinite dimensional kernel, Recent Advances in Differential Equations (Trieste 1978), pp. 295–307, Academic Press, New York, 1981.
  • [16] E. Zeidler, Nonlinear Functional Analysis and its Applications. I, Springer, New York, 1985.
  • [17] E. Zeidler, Nonlinear Functional Analysis and its Applications II/B, Springer, New York, 1990
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

İn-sook Kim

Yayımlanma Tarihi 30 Nisan 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 2 Sayı: 1

Kaynak Göster

APA Kim, İ.-s. (2019). Semilinear problems involving nonlinear operators of monotone type. Results in Nonlinear Analysis, 2(1), 25-35.
AMA Kim İs. Semilinear problems involving nonlinear operators of monotone type. RNA. Nisan 2019;2(1):25-35.
Chicago Kim, İn-sook. “Semilinear Problems Involving Nonlinear Operators of Monotone Type”. Results in Nonlinear Analysis 2, sy. 1 (Nisan 2019): 25-35.
EndNote Kim İ-s (01 Nisan 2019) Semilinear problems involving nonlinear operators of monotone type. Results in Nonlinear Analysis 2 1 25–35.
IEEE İ.-s. Kim, “Semilinear problems involving nonlinear operators of monotone type”, RNA, c. 2, sy. 1, ss. 25–35, 2019.
ISNAD Kim, İn-sook. “Semilinear Problems Involving Nonlinear Operators of Monotone Type”. Results in Nonlinear Analysis 2/1 (Nisan 2019), 25-35.
JAMA Kim İ-s. Semilinear problems involving nonlinear operators of monotone type. RNA. 2019;2:25–35.
MLA Kim, İn-sook. “Semilinear Problems Involving Nonlinear Operators of Monotone Type”. Results in Nonlinear Analysis, c. 2, sy. 1, 2019, ss. 25-35.
Vancouver Kim İ-s. Semilinear problems involving nonlinear operators of monotone type. RNA. 2019;2(1):25-3.