一类带参数的超线性椭圆型方程边值问题的可解性  

Solvability for Certain Superlinear Elliptic Equation Boundary Value Problem with Parameter

作　　者：李殷杰 钟金标 LI Yinjie;ZHONG Jinbiao(School of Mathematics and Physics,Anqing Normal University,Anqing 246133,China)

机构地区：[1]安庆师范大学数理学院,安徽安庆246133

出　　处：《安庆师范大学学报（自然科学版）》2024年第1期43-46,共4页Journal of Anqing Normal University(Natural Science Edition)

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。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 parameter λ is sufficiently small.At the same time,the nonexistence theorem of the solution under certain conditions is proved.As for applications of the theorem,practical examples are given respectively.

关 键 词：不动点定理 上下解方法 正解 极值原理 

分 类 号：O175[理学—数学]