On the exact multiplicity of stable ground states of non-Lipschitz semilinear elliptic equations for some classes of starshaped sets

Advances in Nonlinear Analysis

article

J.I. Díaz¹  J. Hernández¹  Y.Sh. Ilyasov² 

[1] Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid;Institute of Mathematics of UFRC RAS;Instituto de Matemática e Estatística, Universidade Federal de Goiás

关键词: semilinear elliptic equation;    non-Lipschitz terms;    spectral problem;    Pohozaev identity;    flat and compact support ground states;    sharp multiplicity;   

DOI  :  10.1515/anona-2020-0030

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

We prove the exact multiplicity of flat and compact support stable solutions of an autonomous non-Lipschitz semilinear elliptic equation of eigenvalue type according to the dimension N and the two exponents, 0 < α < β < 1, of the involved nonlinearites. Suitable assumptions are made on the spatial domain Ω where the problem is formulated in order to avoid a possible continuum of those solutions and, on the contrary, to ensure the exact number of solutions according to the nature of the domain Ω . Our results also clarify some previous works in the literature. The main techniques of proof are a Pohozhaev’s type identity and some fibering type arguments in the variational approach.

【 授权许可】

CC BY