Multiplicity results for some nonlinear elliptic problems

Journal of the Australian Mathematical Society

Kuan-Ju Chen¹ 

关键词: primary 35J20;    35J25;   

DOI  :  10.1017/S1446788700008934

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

In this paper, first, we study the existence of the positive solutions of the nonlinear elliptic equations in unbounded domains. The existence is affected by the properties of the geometry and the topology of the domain. We assert that if there exists a (PS)c-sequence with c belonging to a suitable interval depending by the equation, then a ground state solution and a positive higher energy solution exist, too. Next, we study the upper half strip with a hole. In this case, the ground state solution does not exist, however there exists at least a positive higher energy solution.

【 授权许可】

Unknown