Existence of Nontrivial Solutions for Generalized Quasilinear Schrödinger Equations with Critical Growth

<abstract>In this paper, we are concerned with the existence of nontrivial positive solutions for the following generalized quasilinear elliptic equations with critical growth <disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} -{\rm{div}}(g^{p}(u)|\nabla u|^{p-2}\nabla u)+ g^{p-1}(u)g'(u)|\nabla u|^{p}+ V(x)|u|^{p-2}u = h(x, u), \; \; x\in \mathbb{R}^{N}, \end{equation*} $\end{document} </tex-math></disp-formula> where $ N\geq3 $, $ 1 < p < N $. Under some suitable conditions, we prove that the above equation has a nontrivial positive solution by variational methods. To some extent, our results improve and supplement some existing relevant results.</abstract>

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Existence of Nontrivial Solutions for Generalized Quasilinear Schrödinger Equations with Critical Growth

Abstract: We study the following generalized quasilinear Schrödinger equations with critical growth −div(

Cited by 2 publications

References 31 publications

Existence and multiplicity of solutions for generalized quasilinear Schrödinger equations

Existence and multiplicity of solutions for generalized quasilinear Schrödinger equations

Existence of nontrivial positive solutions for generalized quasilinear elliptic equations with critical exponent

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