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- Title
Existence and Nonexistence of Solution for a Class of Quasilinear Schrödinger Equations with Critical Growth.
- Authors
Severo, Uberlandio B.; de S. Germano, Diogo
- Abstract
In this work, we study the existence and nonexistence of solution for the following class of quasilinear Schrödinger equations: − div (g 2 (u) ∇ u) + g (u) g ′ (u) | ∇ u | 2 + V (x) u = f (x , u) + h (x) g (u) in R N , <graphic href="10440_2021_412_Article_Equa.gif"></graphic> where N ≥ 3 , g : R → R + is a continuously differentiable function, V (x) is a potential that can change sign, the function h (x) belongs to L 2 N / (N + 2) (R N) and the nonlinearity f (x , s) is possibly discontinuous and may exhibit critical growth. In order to obtain the nonexistence result, we deduce a Pohozaev identity and the existence of solution is proved by means of a fixed point theorem.
- Publication
Acta Applicandae Mathematicae, 2021, Vol 173, Issue 1, p1
- ISSN
0167-8019
- Publication type
Article
- DOI
10.1007/s10440-021-00412-7