Existence of Solutions to a p-Laplacian Equation with Integral Initial Condition

Existence of Solutions to a p-Laplacian Equation

with Integral Initial Condition

SONG WEN-jING1,CAO CHUN-LING2AND ZHAO ZHI-QIANG3

【摘 要】Abstract:In this paper,a class of one-dimension p-Laplacian equation with nonlocal initial value is studied.The existence of solutions to such a problem is obtained by using the topological degree method. 【期刊名称】数学研究通讯 【年(卷),期】2017(033)004 【总页数】7

【关键词】Key words:integral initial condition,existence,topological Communicated by Gao Wen-jie

1 Introduction

Boundary value problems with integral boundary conditions in the ordinary differential equations arise in different areas of applied mathematics and physics.For example,heat conduction,chemical engineering,underground water flow,thermo-elasticity and plasma physics can be reduced to nonlocal problems with integral boundary conditions.For boundary-value problems with integral boundary conditions and comments on their importance,we refer the readers to[1]–[4]and the references therein.For more information about the general theory of integral equations and their relation with boundary-value problems,readers may refer to[5]–[7].