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Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 9
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Research Article

Generalized quasilinear equations with sign-changing unbounded potential

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Pages 3192-3209 | Received 07 Aug 2020, Accepted 01 Oct 2020, Published online: 20 Oct 2020
 

Abstract

We are interested in studying the existence of solution for the generalized quasilinear Schrödinger equation: (P) div(g2(u)u)+g(u)g(u)|u|2+V(x)u=h(x,u),uH1(RN)(P) in RN, where N 3, g and h are suitable smooth functions and V is a potential that may change sign and be unbounded. By using a change of variables and variational arguments, we obtain the existence of a nontrivial solution for the given problem.

2010 Mathematics Subject Classifications:

Acknowledgments

Part of this work was done while the authors were visiting the Universidade de Brasília; they would like to thank Professor Ricardo Ruviaro and all faculty and staff of UnB for their hospitality.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The second author was partially supported by FAPEMA.

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