不连续二阶周期边值问题的可解性

考察了一类非线性项含有一阶导数的二阶周期边值问题的解的存在性,其中非线性项是Carathèodory函数.通过构造非线性项的高度函数并且利用Leray-Schauder不动点定理建立了两个存在定理.第一个定理表明只要高度函数的积分是适当的,这类问题至少有一个解.第二个定理表明当非线性项在无穷远处增长的极限是一个无界函数时在适当条件下这问题仍可能有一个解.

Solvability of Discontinuous Second- Order Periodic Boundary Value Problems

The existence of solution is studied for a class of ,second - order periodic boundary value problems with first derivative, where nonlinear term is a Caratheodory function, By constructing the height functions of nonlinear term and applying Leray - Sehauder fixed point theorem, two existence theorems are established. First theorem shows thai the class of problems has at least one solution provided the integral of height function is appropriate, Second theorem shows thai the existence of solution is Possible under suitable conditions when the limit of growth of nonlinear term at infinity is an unbounded function,