Positive and sign-changing solutions for a quasilinear Steklov nonlinear boundary problem with critical growth

Autor: Liamidi Leadi, Mabel Cuesta
Rok vydání: 2020
Předmět:
Zdroj: Nonlinear Differential Equations and Applications NoDEA. 28
ISSN: 1420-9004
1021-9722
DOI: 10.1007/s00030-020-00666-4
Popis: In this work we study the existence of positive solutions and nodal solutions for the following p-Laplacian problem with Steklov boundary conditions on a bounded regular domain $$\Omega \subset {\mathbb {R}}^N$$ , $$\begin{aligned} \left\{ \begin{array}{ll} -\Delta _p u+V(x)|u|^{p-2}u =0 &{}\quad \hbox { in } \Omega ;\\ |\nabla u|^{p-2}\frac{\partial u}{\partial \nu }=\lambda a(x)|u|^{p-2}u +b(x)|u|^{p_* -2}u &{}\quad \hbox { on }\partial \Omega ; \\ \end{array} \right. \end{aligned}$$ with given numbers p, N satisfying $$1 \max \{p^2, 2p, \frac{p}{p-1}, 2 \}.$$ Our results show striking differences between the cases $$p>2, p=2$$ and $$p
Databáze: OpenAIRE
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