Nehari manifold approach for superlinear double phase problems with variable exponents

被引：0
作者：
Ángel Crespo-Blanco
Patrick Winkert
机构：
[1] Technische Universität Berlin,Institut für Mathematik
来源：
Annali di Matematica Pura ed Applicata (1923 -) | 2024年 / 203卷
关键词：
Double phase operator with variable exponent; Existence of solutions; Multiple solutions; Mountain pass theorem; Nehari manifold; 35A01; 35J20; 35J25; 35J62; 35J92;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper we consider quasilinear elliptic equations driven by the variable exponent double phase operator with superlinear right-hand sides. Under very general assumptions on the nonlinearity, we prove a multiplicity result for such problems whereby we show the existence of a positive solution, a negative one and a solution with changing sign. The sign-changing solution is obtained via the Nehari manifold approach and, in addition, we can also give information on its nodal domains.
引用
收藏
页码：605 / 634
页数：29
相关论文
共 100 条
  • [1] Aberqi A(2022)Existence results for double phase problem in Sobolev-Orlicz spaces with variable exponents in complete manifold Mediterr. J. Math. 19 158-222
  • [2] Bennouna J(2022)Gradient and parameter dependent Dirichlet (p(x), q(x))-Laplace type problem Mathematics 10 1336-379
  • [3] Benslimane O(2020)Double phase problems with variable growth and convection for the Baouendi-Grushin operator Z. Angew. Math. Phys. 71 183-1034
  • [4] Ragusa MA(2015)Harnack inequalities for double phase functionals Nonlinear Anal. 121 206-236
  • [5] Albalawi KS(2016)Non-autonomous functionals, borderline cases and related function classes St. Petersburg Math. J. 27 347-463
  • [6] Alharthi NH(2018)Regularity for general functionals with double phase Calc. Var. Partial Differ. Equ. 57 48-1959
  • [7] Vetro F(2020)Lipschitz bounds and nonuniform ellipticity Comm. Pure Appl. Math. 73 944-273
  • [8] Bahrouni A(2019)Optimal Lipschitz criteria and local estimates for non-uniformly elliptic problems, Atti Accad Naz. Lincei Rend. Lincei Mat. Appl. 30 223-496
  • [9] Rădulescu VD(2021)Symmetry and monotonicity of singular solutions of double phase problems J. Differ. Equ. 280 435-228
  • [10] Winkert P(2016)Eigenvalues for double phase variational integrals Ann. Mat. Pura Appl. 195 1917-1057
12345678910