Open Access Research

Existence results for a class of nonlocal problems involving p-Laplacian

Yang Yang1* and Jihui Zhang2

Author Affiliations

1 School of Science, Jiangnan University, Wuxi, 214122, People's Republic of China

2 Institute of Mathematics, School of Mathematics Science, Nanjing Normal University, Nanjing, 210097, People's Republic of China

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Boundary Value Problems 2011, 2011:32  doi:10.1186/1687-2770-2011-32

Published: 11 October 2011

Abstract

This paper is concerned with the existence of solutions to a class of p-Kirchhoff type equations with Neumann boundary data as follows:

<a onClick="popup('http://www.boundaryvalueproblems.com/content/2011/1/32/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2011/1/32/mathml/M1">View MathML</a>

By means of a direct variational approach, we establish conditions ensuring the existence and multiplicity of solutions for the problem.

Keywords:
Nonlocal problems; Neumann problem; p-Kirchhoff's equation