## Taiwanese Journal of Mathematics

### Existence and Multiplicity of Solutions for a Class of $(p,q)$-Laplacian Equations in $\mathbb{R}^N$ with Sign-changing Potential

#### Abstract

In this paper, we use variational approaches to establish the existence of weak solutions for a class of $(p,q)$-Laplacian equations on $\mathbb{R}^N$, for $1 \lt q \lt p \lt q^{*} := Nq/(N-q)$, $p \lt N$, with a sign-changing potential function and a Carathéodory reaction term which do not satisfy the Ambrosetti-Rabinowitz type growth condition. By linking theorem with Cerami condition, the fountain theorem and dual fountain theorem with Cerami condition, we obtain some existence of weak solutions for the above equations under our considerations which are different from those used in related papers.

#### Article information

Source
Taiwanese J. Math., Volume 24, Number 1 (2020), 159-178.

Dates
Revised: 21 February 2019
Accepted: 12 March 2019
First available in Project Euclid: 1 April 2019

https://projecteuclid.org/euclid.twjm/1554105651

Digital Object Identifier
doi:10.11650/tjm/190302

Mathematical Reviews number (MathSciNet)
MR4053843

Zentralblatt MATH identifier
07175545

Subjects
Primary: 35A15: Variational methods 35J62: Quasilinear elliptic equations

#### Citation

Zhang, Nian; Jia, Gao. Existence and Multiplicity of Solutions for a Class of $(p,q)$-Laplacian Equations in $\mathbb{R}^N$ with Sign-changing Potential. Taiwanese J. Math. 24 (2020), no. 1, 159--178. doi:10.11650/tjm/190302. https://projecteuclid.org/euclid.twjm/1554105651

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