四阶拟线性微分方程非线性边值问题解的存在性

Existence Of Solutions for Nonlinear Boundary Value Problems of the Fourth Order Quasilinear Differential Equations

本文研究了四阶拟线性微分方程非线性边值问题(φp(u))′=f(t,u,u″),u(0)=A,u′(0)=B,g(u″(0),u″(1))=0,h(u″(0),u″(1),u(0),u(1))=0,解的存在性。此问题借鉴p-拉普拉斯方程,一般化的反应扩散理论,非牛顿流体理论和多孔介质中的气体湍流等问题的研究成果,利用上下解方法得到此方程非线性边值问题解的存在性。本研究结果是新的且推广了已有研究成果。

This article studied the existence of solutions for nonlinear boundary value problems of the fourth order quasilinear differential equations Through making ues of the research results of p - laplace equation, generalized diffusion theory, non - Newtonian fluid theory, and the turbulent flow of a gas in porous medium, this study obtained the the existence of solutions for nonlinear boundary value problems of the fourth order quasilinear differential equations. The results of this paper are new and extende previously known results.