Multiplicity of positive solutions for the Kirchhoff-type equations with critical exponent in RN期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Multiplicity of positive solutions for the Kirchhoff-type equations with critical exponent in RN

Authors:	OH Miyagaki LC Paes-Leme BM Rodrigues

Affiliation:	1. Departamento de Matemática, Universidade Federal de Juiz de Fora, Juiz de Fora, MG, 36.036-000, Brazil;2. Departamento de Matemática, Universidade Federal de Ouro Preto, Ouro Preto, MG, 35.400-000, Brazil

Abstract:	In this work we study the existence and multiplicity of solutions to the following Kirchhoff-type problem with critical nonlinearity in $R^{N}$ $\{\begin{matrix} ? (a + b \int_{R^{N}} {\|? u\|}^{p} d x) Δ_{p} u = μ u^{p^{1} ? 1} + λ f (x, u); x \in R^{N}, \\ u \in D^{1, p} (R^{N}), \end{matrix} is=$ where $N \geq 2 p$ , $μ, λ, a, b > 0$ and the nonlinearity $f (x, u)$ satisfies certain subcritical growth conditions. By using topological and variational methods, infinitely many positive solutions are obtained.

Keywords:	Kirchhoff-type Variational methods Critical exponents Corresponding author
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