一类四阶非线性常微分方程两点边值问题三重正解的存在性

考虑一类四阶非线性两点边值问题三重正解的存在性问题,这里f:[0,1]×[0,+∞)×(-∞,0]→[0,+∞).通过适当变换可将上述四阶边值问题转化为与其等价的二阶微分-积分方程的两点边值问题,适当定义半序巴拿赫空间及其上的锥,运用Legget-Williams不动点定理,得到二阶微分-积分方程的两点边值问题的三重正解的存在性,再由等价性,得到上述四阶非线性两点边值问题三重正解的存在性.

Existence of Triple Positive Solutions to A Class of Nonlinear Fourth-Order Two-Point Boundary Value Problem

In this paper,the existence of at least three positive solutions to a class of nonlinear fourth order two- point boundary value problem is considered:Where is continuous.We exploit the fact that the above boundary value problem can be translated to a second order integral-differential boundary value problem.The Legget -Williams fixed point theorem is applyed in cone to the equivalent second order integral-differential boundary value proble,and get the existence of at least three positive solutions for the second order integraldifferential boundary value problem.So the existence of at least three positive solutions for the above nonlinear fourth order two-point boundary value problem is proved by the equivalence property.