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February, 2020 Existence and Multiplicity of Solutions for a Class of $(p,q)$-Laplacian Equations in $\mathbb{R}^N$ with Sign-changing Potential
Nian Zhang, Gao Jia
Taiwanese J. Math. 24(1): 159-178 (February, 2020). DOI: 10.11650/tjm/190302

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.

Citation

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Nian Zhang. Gao Jia. "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 (1) 159 - 178, February, 2020. https://doi.org/10.11650/tjm/190302

Information

Received: 17 October 2018; Revised: 21 February 2019; Accepted: 12 March 2019; Published: February, 2020
First available in Project Euclid: 1 April 2019

zbMATH: 07175545
MathSciNet: MR4053843
Digital Object Identifier: 10.11650/tjm/190302

Subjects:
Primary: 35A15 , 35J62

Keywords: $(p,q)$-Laplacian , Cerami condition , dual Fountain theorem , Fountain Theorem , linking theorem

Rights: Copyright © 2020 The Mathematical Society of the Republic of China

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Vol.24 • No. 1 • February, 2020
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