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Existence of positive solutions for a class of p-Laplacian type generalized quasilinear Schrödinger equations with critical growth and potential vanishing at infinity.
- Source :
-
Electronic Journal of Qualitative Theory of Differential Equations . 2023, p1-20. 20p. - Publication Year :
- 2023
-
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), x ∈ RN, 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) =∫u0g(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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *MOUNTAIN pass theorem
*CONTINUOUS functions
*SCHRODINGER equation
Subjects
Details
- Language :
- English
- ISSN :
- 14173875
- Database :
- Academic Search Index
- Journal :
- Electronic Journal of Qualitative Theory of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 175272511
- Full Text :
- https://doi.org/10.14232/ejqtde.2023.1.3