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March/April 2020 Infinitely many solutions for a class of superlinear problems involving variable exponents
Bin Ge, Li-Yan Wang
Adv. Differential Equations 25(3/4): 191-212 (March/April 2020).

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.

Citation

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Bin Ge. Li-Yan Wang. "Infinitely many solutions for a class of superlinear problems involving variable exponents." Adv. Differential Equations 25 (3/4) 191 - 212, March/April 2020.

Information

Published: March/April 2020
First available in Project Euclid: 21 March 2020

zbMATH: 07198961
MathSciNet: MR4079792

Subjects:
Primary: 35J60, 35J70, 58E05

Rights: Copyright © 2020 Khayyam Publishing, Inc.

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Vol.25 • No. 3/4 • March/April 2020
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