Existence, concentration and multiplicity of solutions for (p,N)-Laplacian equations with convolution term
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Published:2024-08-20
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Volume:
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ISSN:1664-3607
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Container-title:Bulletin of Mathematical Sciences
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language:en
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Short-container-title:Bull. Math. Sci.
Author:
Li Yiqing1ORCID,
Van Nguyen Thin2ORCID,
Zhang Binlin1ORCID
Affiliation:
1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, P. R. China
2. Department of Mathematics, Thai Nguyen University of Education, Thai Nguyen, Vietnam
Abstract
In this paper, we concern some qualitative properties of the following [Formula: see text]-Laplacian equations with convolution term: [Formula: see text] where [Formula: see text] is a positive parameter, [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] satisfies the critical exponential growth. By using the variational methods and the penalization method, we prove the existence of solutions for the above equations which concentrates at a local minimum of [Formula: see text] in the semi-classical limit as [Formula: see text]. Moreover, we obtain the multiplicity of solutions for the above equations by the Morse theory.
Funder
National Natural Science Foundation of China
Shandong Provincial Natural Science Foundation, P. R. China
Publisher
World Scientific Pub Co Pte Ltd