The existence of multiple positive solutions of p-Laplacian boundary value problems

Mathematica Slovaca

Yuji Liu¹ 

关键词: one-dimension p-Laplacian;    differential equation;    nonlocal boundary value problem;    positive solution;    fixed point theorem;   

DOI  :  10.2478/s12175-007-0019-2

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

In this paper, we establish sufficient conditions to guarantee the existence of at least three or 2n − 1 positive solutions of nonlocal boundary value problems consisting of the second-order differential equation with p-Laplacian (1)$$[phi _p (x'(t))]' + f(t,x(t)) = 0, t in (0,1),$$ and one of following boundary conditions (2)$$x(0) = intlimits_0^1 {x(s) dh(s),} phi _p (x'(1)) = intlimits_0^1 {phi _p (x'(s)) dg(s)} ,$$ and (3)$$phi _p (x'(0)) = intlimits_0^1 {phi _p (x'(s)) dh(s),} x(1) = intlimits_0^1 {x(s) dg(s)} .$$ Examples are presented to illustrate the main results.

【 授权许可】

Unknown