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Optimizing solutions with competing anisotropic (p, q)-Laplacian in hemivariational inequalities

Yıl 2024, , 150 - 159, 15.12.2024
https://doi.org/10.33205/cma.1566388

Öz

For differential inclusions and hemivariational inequalities driven by anisotropic differential operators, we establish the existence of generalized variational solutions and weak solutions. The main novelty consists in allowing that the driving operators might not satisfy any ellipticity condition, which is achieved for the first time in the anisotropic and nonsmooth context. The approach is based on a finite dimensional approximation process.

Proje Numarası

0

Kaynakça

  • M. Allalou, M. El Ouaarabi and A. Raji: On a class of nonhomogeneous anisotropic elliptic problem with variable exponents, Rend. Circ. Mat. Palermo, II. Ser (2024).
  • M. Bohner, G. Caristi, A. Ghobadi and Sh. Heidarkhani: Three solutions for discrete anisotropic Kirchhoff-type problems, Demonstr. Math., 56 (1) (2023), Article ID: 20220209.
  • G. Bonanno, G. D’Aguì and A. Sciammetta: Multiple solutions for a class of anisotropic −→p -Laplacian problems, Bound. Value Probl., 2023 (2023), Article ID: 89.
  • B. Brandolini, F. Cîrstea: Anisotropic elliptic equations with gradient-dependent lower order terms and L1 data, Math. Eng., 5 (4) (2023), 1–33.
  • B. Brandolini, F. Cîrstea: Boundedness of solutions to singular anisotropic elliptic equations, Discrete Contin. Dyn. Syst. Ser. S, 17 (4) (2024), 1545–1561.
  • H. Brezis: Functional analysis, Sobolev spaces and partial differential equations, Universitext, Springer, New York (2011).
  • A. Cernea: On the solutions of a coupled system of proportional fractional differential inclusions of Hilfer type, Modern Math. Methods, 2 (2) (2024), 80–89.
  • K. C. Chang: Variational methods for non-differentiable functionals and their applications to partial differential equations, J. Math. Anal. Appl., 80 (1981), 102–129.
  • F. H. Clarke: Optimization and Nonsmooth Analysis, John Wiley & Sons, Inc., New York, USA (1983).
  • I. Fragalà, F. Gazzola and B. Kawohl: Existence and nonexistence results for anisotropic quasilinear elliptic equations, Ann. Inst. H. Poincaré C Anal. Non Linéaire, 21 (5) (2004), 715–734.
  • L. Gambera, S. A. Marano and D. Motreanu: Quasi-linear Dirichlet systems with competing operators and convection, J. Math. Anal. Appl., 530 (2024), Article ID: 127718.
  • Z. Liu, R. Livrea, D. Motreanu and S. Zeng: Variational differential inclusions without ellipticity condition, Electron. J. Qual. Theory Differ. Equ., 43 (2020), 1–17.
  • M. Mih˘ailescu, P. Pucci and V. D. R˘adulescu: Eigenvalue problems for anisotropic quasilinear elliptic equations with varaible exponent, J. Math. Anal. Appl., 340 (2008), 687–698.
  • D. Motreanu: Quasilinear Dirichlet problems with competing operators and convection, Open Math., 18 (2020), 1510–1517.
  • D. Motreanu: Systems of hemivariational inclusions with competing operators, Mathematics, 12 (11) (2024), Article ID: 1766.
  • D. Motreanu: Hemivariational inequalities with competing operators, Commun. Nonlinear Sci. Numer. Simulat., 130 (2024), Article ID: 107741.
  • D. Motreanu, A. Razani: Competing anisotropic and Finsler (p, q)-Laplacian problems, Bound. Value Probl., 2024 (2024), Article ID: 39.
  • D. Motreanu, E. Tornatore: Dirichlet problems with anisotropic principal part involving unbounded coefficients, Electron. J. Differential Equations, 2024 (11) (2024), 1–13.
  • A. Razani: Nonstandard competing anisotropic (p, q)-Laplacians with convolution, Bound. Value Probl., 2022 (2022), Article ID: 87.
  • A. Razani: Entire weak solutions for an anisotropic equation in the Heisenberg group, Proc. Amer. Math. Soc., 151 (11) (2023), 4771–4779.
  • A. Razani: Competing Kohn-Spencer Laplacian systems with convection in non-isotropic Folland-Stein space, Complex Var. Elliptic Equ., (2024), 1–14. DOI: 10.1080/17476933.2024.2337868
  • A. Razani, G. S. Costa and G. M. Figueiredo: A positive solution for a weighted anisotropic p-Laplace equation involving vanishing potential, Mediterr. J. Math., 21 (2024), Article ID: 59.
  • A. Razani, G. M. Figueiredo: Degenerated and competing anisotropic (p, q)-Laplacians with weights, Appl. Anal., 102 (2023), 4471–4488.
  • A. Razani, G. M. Figueiredo: A positive solution for an anisotropic (p, q)-Laplacian, Discrete Contin. Dyn. Syst. Ser. S, 16 (6) (2023), 1629–1643.
  • A. Razani, G. M. Figueiredo: Infinitely many solutions for an anisotropic differential inclusion on unbounded domains, Electron. J. Qual. Theory Differ. Equ., 33 (2024), 1–17.
  • A. Razani, E. Tornatore: Solutions for nonhomogeneous degenerate quasilinear anisotropic problems, Constr. Math. Anal., 7 (3) (2024), 134–149.
Yıl 2024, , 150 - 159, 15.12.2024
https://doi.org/10.33205/cma.1566388

Öz

Proje Numarası

0

Kaynakça

  • M. Allalou, M. El Ouaarabi and A. Raji: On a class of nonhomogeneous anisotropic elliptic problem with variable exponents, Rend. Circ. Mat. Palermo, II. Ser (2024).
  • M. Bohner, G. Caristi, A. Ghobadi and Sh. Heidarkhani: Three solutions for discrete anisotropic Kirchhoff-type problems, Demonstr. Math., 56 (1) (2023), Article ID: 20220209.
  • G. Bonanno, G. D’Aguì and A. Sciammetta: Multiple solutions for a class of anisotropic −→p -Laplacian problems, Bound. Value Probl., 2023 (2023), Article ID: 89.
  • B. Brandolini, F. Cîrstea: Anisotropic elliptic equations with gradient-dependent lower order terms and L1 data, Math. Eng., 5 (4) (2023), 1–33.
  • B. Brandolini, F. Cîrstea: Boundedness of solutions to singular anisotropic elliptic equations, Discrete Contin. Dyn. Syst. Ser. S, 17 (4) (2024), 1545–1561.
  • H. Brezis: Functional analysis, Sobolev spaces and partial differential equations, Universitext, Springer, New York (2011).
  • A. Cernea: On the solutions of a coupled system of proportional fractional differential inclusions of Hilfer type, Modern Math. Methods, 2 (2) (2024), 80–89.
  • K. C. Chang: Variational methods for non-differentiable functionals and their applications to partial differential equations, J. Math. Anal. Appl., 80 (1981), 102–129.
  • F. H. Clarke: Optimization and Nonsmooth Analysis, John Wiley & Sons, Inc., New York, USA (1983).
  • I. Fragalà, F. Gazzola and B. Kawohl: Existence and nonexistence results for anisotropic quasilinear elliptic equations, Ann. Inst. H. Poincaré C Anal. Non Linéaire, 21 (5) (2004), 715–734.
  • L. Gambera, S. A. Marano and D. Motreanu: Quasi-linear Dirichlet systems with competing operators and convection, J. Math. Anal. Appl., 530 (2024), Article ID: 127718.
  • Z. Liu, R. Livrea, D. Motreanu and S. Zeng: Variational differential inclusions without ellipticity condition, Electron. J. Qual. Theory Differ. Equ., 43 (2020), 1–17.
  • M. Mih˘ailescu, P. Pucci and V. D. R˘adulescu: Eigenvalue problems for anisotropic quasilinear elliptic equations with varaible exponent, J. Math. Anal. Appl., 340 (2008), 687–698.
  • D. Motreanu: Quasilinear Dirichlet problems with competing operators and convection, Open Math., 18 (2020), 1510–1517.
  • D. Motreanu: Systems of hemivariational inclusions with competing operators, Mathematics, 12 (11) (2024), Article ID: 1766.
  • D. Motreanu: Hemivariational inequalities with competing operators, Commun. Nonlinear Sci. Numer. Simulat., 130 (2024), Article ID: 107741.
  • D. Motreanu, A. Razani: Competing anisotropic and Finsler (p, q)-Laplacian problems, Bound. Value Probl., 2024 (2024), Article ID: 39.
  • D. Motreanu, E. Tornatore: Dirichlet problems with anisotropic principal part involving unbounded coefficients, Electron. J. Differential Equations, 2024 (11) (2024), 1–13.
  • A. Razani: Nonstandard competing anisotropic (p, q)-Laplacians with convolution, Bound. Value Probl., 2022 (2022), Article ID: 87.
  • A. Razani: Entire weak solutions for an anisotropic equation in the Heisenberg group, Proc. Amer. Math. Soc., 151 (11) (2023), 4771–4779.
  • A. Razani: Competing Kohn-Spencer Laplacian systems with convection in non-isotropic Folland-Stein space, Complex Var. Elliptic Equ., (2024), 1–14. DOI: 10.1080/17476933.2024.2337868
  • A. Razani, G. S. Costa and G. M. Figueiredo: A positive solution for a weighted anisotropic p-Laplace equation involving vanishing potential, Mediterr. J. Math., 21 (2024), Article ID: 59.
  • A. Razani, G. M. Figueiredo: Degenerated and competing anisotropic (p, q)-Laplacians with weights, Appl. Anal., 102 (2023), 4471–4488.
  • A. Razani, G. M. Figueiredo: A positive solution for an anisotropic (p, q)-Laplacian, Discrete Contin. Dyn. Syst. Ser. S, 16 (6) (2023), 1629–1643.
  • A. Razani, G. M. Figueiredo: Infinitely many solutions for an anisotropic differential inclusion on unbounded domains, Electron. J. Qual. Theory Differ. Equ., 33 (2024), 1–17.
  • A. Razani, E. Tornatore: Solutions for nonhomogeneous degenerate quasilinear anisotropic problems, Constr. Math. Anal., 7 (3) (2024), 134–149.
Toplam 26 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Temel Matematik (Diğer)
Bölüm Makaleler
Yazarlar

Dumitru Motreanu Bu kişi benim 0000-0001-7391-9534

Abdolrahman Razani 0000-0002-3092-3530

Proje Numarası 0
Erken Görünüm Tarihi 28 Kasım 2024
Yayımlanma Tarihi 15 Aralık 2024
Gönderilme Tarihi 13 Ekim 2024
Kabul Tarihi 24 Kasım 2024
Yayımlandığı Sayı Yıl 2024

Kaynak Göster

APA Motreanu, D., & Razani, A. (2024). Optimizing solutions with competing anisotropic (p, q)-Laplacian in hemivariational inequalities. Constructive Mathematical Analysis, 7(4), 150-159. https://doi.org/10.33205/cma.1566388
AMA Motreanu D, Razani A. Optimizing solutions with competing anisotropic (p, q)-Laplacian in hemivariational inequalities. CMA. Aralık 2024;7(4):150-159. doi:10.33205/cma.1566388
Chicago Motreanu, Dumitru, ve Abdolrahman Razani. “Optimizing Solutions With Competing Anisotropic (p, Q)-Laplacian in Hemivariational Inequalities”. Constructive Mathematical Analysis 7, sy. 4 (Aralık 2024): 150-59. https://doi.org/10.33205/cma.1566388.
EndNote Motreanu D, Razani A (01 Aralık 2024) Optimizing solutions with competing anisotropic (p, q)-Laplacian in hemivariational inequalities. Constructive Mathematical Analysis 7 4 150–159.
IEEE D. Motreanu ve A. Razani, “Optimizing solutions with competing anisotropic (p, q)-Laplacian in hemivariational inequalities”, CMA, c. 7, sy. 4, ss. 150–159, 2024, doi: 10.33205/cma.1566388.
ISNAD Motreanu, Dumitru - Razani, Abdolrahman. “Optimizing Solutions With Competing Anisotropic (p, Q)-Laplacian in Hemivariational Inequalities”. Constructive Mathematical Analysis 7/4 (Aralık 2024), 150-159. https://doi.org/10.33205/cma.1566388.
JAMA Motreanu D, Razani A. Optimizing solutions with competing anisotropic (p, q)-Laplacian in hemivariational inequalities. CMA. 2024;7:150–159.
MLA Motreanu, Dumitru ve Abdolrahman Razani. “Optimizing Solutions With Competing Anisotropic (p, Q)-Laplacian in Hemivariational Inequalities”. Constructive Mathematical Analysis, c. 7, sy. 4, 2024, ss. 150-9, doi:10.33205/cma.1566388.
Vancouver Motreanu D, Razani A. Optimizing solutions with competing anisotropic (p, q)-Laplacian in hemivariational inequalities. CMA. 2024;7(4):150-9.