Positive Pseudo-Symmetric Solution For a Nonlocal p-Laplacian Boundary value Problem

L. X. Truong, P. D. Dung, B. T. Quan,
Differential Equations & Application, 2013, Volumn 5, Number 1 pp 53-68

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Abstract

This paper is devoted to the study of the following nonlocal p-Laplacian functional differential equation − φp(x (t)) = λ f(t,x(t),x (t))  1 0 f(s,x(s),x (s))dsn , 0 < t < 1, subject to multi point boundary conditions. We obtain some results on the existence of at least one (when n ∈ Z+ ) or triple (when n = 0 ) pseudo-symmetric positive solutions by using fixedpoint theory in cone.

Keywords: boundary value problem, pseudo-symmetric solutions, p-Laplacian, LeggettWilliams fixed point theorem, Guo-Krasnoselskii fixed point theorem.