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

Nian Zhang and Gao Jia

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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

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

Received: 17 October 2018
Revised: 21 February 2019
Accepted: 12 March 2019
First available in Project Euclid: 1 April 2019

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Zentralblatt MATH identifier

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

$(p,q)$-Laplacian Cerami condition linking theorem fountain theorem dual fountain theorem


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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