一类带有积分边界条件和变号非线性项的四阶p-Laplacian微分方程解的存在唯一性

Existence and Uniqueness of Solutions for Fourth-Order p-Laplacian Differential Equations with Integral Boundary Conditions and a Sign-Changing Nonlinear Term

利用上下解方法和Leray-Schauder度理论,研究了四阶p-Laplacian微分方程(Φ(u'''(t)))'-f(t,u(t),u'(t),u″(t),u'''(t))=0,t∈(0,1)在积分边界条件下解的存在性和唯一性.其中f:[0,1]×R^4→R为连续函数,Φ(u)为增同胚且Φ(0)=0,Φ(R)=R,R=(-∞,+∞).

By the method of upper and lower solutions and Leary-Schauder degree theory, we investigate the existence and uniqueness of a solutions for the following four order differential equation （Φ（u＇＇＇（t）））＇-f（t,u（t）,u＇（t）,u″（t）,u＇＇＇（t））=0,t∈（0,1） subject to the integral boundary conditions, f：[0,1]×R^4→R are continuous and Ф （u） is an increasing homeomorphism with Φ（0）=0,Φ（R）=R,R=（-∞,＋∞）.