Advances in Differential Equations

Infinitely many solutions for a class of superlinear problems involving variable exponents

Bin Ge and Li-Yan Wang

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We are concerned with the following $p(x)$-Laplacian equations in $\mathbb{R}^N$ $$ -\triangle_{p(x)} u+V(x)|u|^{p(x)-2}u= f(x,u)\ \ {\rm in }\; \mathbb{R}^N. $$ Based on a direct sum decomposition of a space, we investigate the multiplicity of solutions for the considered problem. The potential $V$ is allowed to be no coerciveness, and the primitive of the nonlinearity $f$ is of super-$p^+$ growth near infinity in $u$ and allowed to be sign-changing. Our assumptions are suitable and different from those studied previously.

Article information

Source
Adv. Differential Equations, Volume 25, Number 3/4 (2020), 191-212.

Dates
First available in Project Euclid: 21 March 2020

Permanent link to this document
https://projecteuclid.org/euclid.ade/1584756039

Mathematical Reviews number (MathSciNet)
MR4079792

Zentralblatt MATH identifier
07198961

Subjects
Primary: 35J60: Nonlinear elliptic equations 35J70: Degenerate elliptic equations 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)

Citation

Ge, Bin; Wang, Li-Yan. Infinitely many solutions for a class of superlinear problems involving variable exponents. Adv. Differential Equations 25 (2020), no. 3/4, 191--212. https://projecteuclid.org/euclid.ade/1584756039


Export citation