Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774060 | Journal of Differential Equations | 2017 | 31 Pages |
Abstract
We study the existence and nonexistence of nonzero solutions for the following class of quasilinear Schrödinger equations:âÎu+V(x)u+κ2[Î(u2)]u=h(u),xâRN, where κ>0 is a parameter, V(x) is a continuous potential which is large at infinity and the nonlinearity h can be asymptotically linear or superlinear at infinity. In order to prove our existence result we have applied minimax techniques together with careful Lâ-estimates. Moreover, we prove a Pohozaev identity which justifies that 2â=2N/(Nâ2) is the critical exponent for this class of problems and it is also used to show nonexistence results.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Uberlandio B. Severo, Elisandra Gloss, Edcarlos D. da Silva,