摘要
本文研究了一类椭圆型方程Dirichlet边值问题的可解性,其中,非线性项包含了线性部分、参数及在无穷远处为超线性的部分.利用不动点定理及上下解方法来证明了该问题在参数λ充分小时正解的存在性;在非线性项满足Lipschitz连续及参数λ充分小时解的唯一性定理;同时论证了在一定条件下解的不存在性定理.最后分别给出了定理的应用实例.
Abstract
In this paper,we study the solvability of a class of Dirichlet boundar value problem for elliptic equation,in which the nonlinear term contains linear part,parameters and superlinear par-t at infinity.Using the fixed point theorem and method of lower and upper solution,it is proved that the existence of the positive solution when the parameter λ is sufficiently small,and the uniqueness theorem of the solution is proved when the nonlinear term is Lipschitz continuous and the parameterλ is sufficiently small.At the same time,the nonexistence theorem of the solution under certain conditions is proved.As for ap-plications of the theorem,practical examples are given respectively.
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