Existence of Solutions for p-Laplace Equations Subjected to Neumann Boundary Value Problem

The existence of solutions for one dimensional p-Laplace equation (φ p (u ′) )′ = f (t , u , u′) with t ∈ (0,1) and 2 ( ) p φp s s s ? = , s ≠ 0 subjected to Neumann boundary value problem at u′( 0) = 0 ,u′( 1) = 0. By using the degree theory, the sufficient conditions of the existence of solutions for p-Laplace equation subjected to Neumann boundary value condition are established.

The existence of solutions for one dimensional p-Laplace equation （φp（u′））′=f（t,u,u′） with t∈（0,1） and Фp（s）=｜s｜^p-2 s, s≠0 subjected to Neumann boundary value problem at u′（0） = 0, u′（1） = 0. By using the degree theory, the sufficient conditions of the existence of solutions for p-Laplace equation subjected to Neumann boundary value condition are established.