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 (2023) Existence of positive solutions for a class of p-Laplacian type generalized quasilinear Schrödinger equations with critical growth and potential vanishing at infinity. ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2023 (3). pp. 1-20. ISSN 1417-3875

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Abstract

In this paper, we study the existence of positive solutions for the following generalized quasilinear Schrödinger equation −div(gp(u)|∇u|p−2∇u) + gp−1(u)g′(u)|∇u|p +V(x)|u|p−2u =K(x)f(u)+Q(x)g(u)|G(u)|p∗−2G(u), where N ≥ 3, 1 < p ≤ N, p∗ = Np x ∈RN, N−p, g ∈ C1(R,R+), V(x) and K(x) are positive continuous functions and G(u) = 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.

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