Existence of positive solutions for a class of p-Laplacian type generalized quasilinear Schrödinger equations with critical growth and potential vanishing at infinity

Li Zhen: Existence of positive solutions for a class of p-Laplacian type generalized quasilinear Schrödinger equations with critical growth and potential vanishing at infinity. (2023)

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Abstract

In this paper, we study the existence of positive solutions for the following generalized quasilinear Schrödinger equation − div(g p (u)|∇u| p−2∇u) + g p−1 (u)g (u)|∇u| p + V(x)|u| p−2u = K(x)f(u) + Q(x)g(u)|G(u)| p ∗−2G(u), x ∈ R N, where N ≥ 3, 1 < p ≤ N, p Np N−p , g ∈ C1 (R, R+), V(x) and K(x) are positive continuous functions and G(u) = R u 0 g(t)dt. By using a change of variable, we obtain the existence of positive solutions for this problem by using the Mountain Pass Theorem. Our results generalize some existing results.

Item Type: Journal
Publication full: Electronic journal of qualitative theory of differential equations
Date: 2023
Number: 3
ISSN: 1417-3875
Language: English
DOI: 10.14232/ejqtde.2023.1.3
Uncontrolled Keywords: Schrödinger-egyenlet - kvázilineáris
Additional Information: Bibliogr.: p. 17-20. ; összefoglalás angol nyelven
Subjects: 01. Natural sciences
01. Natural sciences > 01.01. Mathematics
Date Deposited: 2023. Mar. 13. 13:05
Last Modified: 2023. Mar. 13. 13:05
URI: http://acta.bibl.u-szeged.hu/id/eprint/78358

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