p(x)-Laplacian equations satisfying Cerami condition

2008

57 citations recorded by the source corpus.

The goal of this paper is to prove the existence and multiplicity of solutions for the p(x)-Laplacian equations without the well-known Ambrosetti–Rabinowitz type growth conditions. The critical point theorems with Cerami condition are used.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/c2d04bba5cb01936969e80f5e339a7c2e2107d07

Citations in the corpus

• VARIABLE BESOV AND TRIEBEL-LIZORKIN SPACES (2008, unknown): “In recent decades, these spaces and the corresponding variable Sobolev spaces W k,p(·) have attracted more attention and have been applied to partial differential equations and the calculus of variations, see [1]–[16], [18], [19], [26], [27].”
• Overview of differential equations with non-standard growth (2010, unknown): “For instance, in [170] the condition 2 of Theorem 6.”
• An atomic decomposition of variable Besov and Triebel-Lizorkin spaces (2009, unknown): “Moreover, these spaces have been applied to partial differential equations and the calculus of variation, see [1, 3, 4, 5, 6, 7, 8, 10, 11, 12, 16, 17, 18, 19, 21, 22, 29] and references therein.”
• Existence and multiplicity of weak solutions for elliptic Dirichlet problems with variable exponent (2014, unknown): “The existence of one weak solution for the problem (Dλ,f ) was investigated for instance in [15] and in [26].”
• A-priori bounds and multiplicity of solutions for nonlinear elliptic problems involving the fractionalp(⋅)-Laplacian (2018, unknown): “finitely many solutions; see also [5,12,15]. As we know, some global assumptions on f(x,u) were used in an essential way to derive the existence of infinitely many solutions for elliptic equations; see [1,4,5,13,14,23]. However the authors in [5,8,12,15,20] investigated the existence of small energy s”