Existence of infinitely many solutions for an anisotropic equation using genus theory

Abstract

Using genus theory, the existence of infinitely many solutions for an anisotropic equation involving the subcritical growth is proved. Also, by using Krasnoselskii genus and Clark's theorem, the existence of k‐pairs of distinct solutions is proved. Finally, the existence of infinitely many solutions for an anisotropic equation involving the critical growth is studied.

Existence of radial weak solutions to Steklov problem involving Leray–Lions type operator

“…Finally, we assume that h ∈ L p � (⋅) (Ω) is a positive continuous function such that |h| p � (⋅) is small enough. Faria et al [4] have studied the existence of positive solutions for the following nonlinear elliptic problems under Dirichlet boundary condition Their approach relies on the method of sub-supersolution and nonlinear regularity theory (see [5,16,17] for sub-supersolution methods). Hai Ha et al [6] have proved the existence of infinitely many solutions for a generalized p(⋅)-Laplace equation involving Leray-Lions operators where Ω is a bounded domain in ℝ N with a Lipchitz boundary Ω ; a ∶ Ω × ℝ N → ℝ N and f ∶ Ω × ℝ → ℝ are Carathéodory functions with suitable growth conditions.…”

Solutions to a $$(p_1, \ldots ,p_n)$$-Laplacian Problem with Hardy Potentials

“…positive in an open set. In 2019, Behboudi et al [2] verified the existence of two weak solutions for the following problem where 2 ≤ q < p < N (one can see [9,10,12,13,17,[20][21][22][23][24][25]33] and references therein for the importance of study of these kinds of problems).…”

A positive solution for an anisotropic $ (p,q) $-Laplacian

“…His work initiated lots of works on the theory of phase transitions, in particular in the case of anisotropic and nonhomogenous media. Recently, there some articles about the existence of solutions for anisotropic problems (see [10,13,19,15,17,20,21,14,37,44] and the references therein).…”