Open AccessPositive solutions for a class of generalized quasilinear Schrödinger equation involving concave and convex nonlinearities in Orilicz space
Author(s) -
Meng Yan,
Xianjiu Huang,
Jianhua Chen
Publication year - 2021
Publication title -
electronic journal on the qualitative theory of differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.524
H-Index - 33
ISSN - 1417-3875
DOI - 10.14232/ejqtde.2021.1.87
Subject(s) - algorithm , materials science , computer science
In this paper, we study the following generalized quasilinearSchrödinger equation − div ( g 2 ( u ) ∇ u ) + g ( u ) g ′ ( u ) | ∇ u | 2 + V ( x ) u = λ f ( x , u ) + h ( x , u ) , x ∈ R N , where λ > 0 , N ≥ 3 , g ∈ C 1 ( R , R + ) . By using a change ofvariable, we obtain the existence of positive solutions for this problemwith concave and convex nonlinearities via the Mountain Pass Theorem. Ourresults generalize some existing results.