A MULTIPLICITY RESULTS TO A p - q LAPLACIAN SYSTEM WITH A CONCAVE AND SINGULAR NONLINEARITIES

被引：0

作者：

Choudhuri, Debajyoti ^{[1
]}

Kratou, Mouna ^{[2
]}

Saoudi, Kamel ^{[2
]}

机构：

[1] Natl Inst Technol Rourkela, Dept Math, Rourkela, India

[2] Imam Abdulrahman Bin Faisal Univ, Basic & Appl Sci Res Ctr, POB 1982, Dammam 31441, Saudi Arabia

来源：

FIXED POINT THEORY | 2023年 / 24卷 / 01期

关键词：

Nehari manifold; Lusternik-Schnirelman category; singularity; multi-plicity; LINEAR ELLIPTIC SYSTEM; POSITIVE SOLUTIONS; EIGENVALUE PROBLEM; EQUATION; EXISTENCE;

D O I：

10.24193/fpt-ro.2023.1.06

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the existence of multiple nontrivial positive weak solutions to the following system of problems. - Delta pu-Delta qu= lambda f(x)|u|r-2u +nu 1 -alpha 2 -alpha - beta h(x)|u|-alpha|v|1-beta in omega, - Delta pv-Delta qv= mu g(x)|v|r-2v +nu 1 -beta 2 -alpha -beta h(x)|u|1-alpha|v|-beta in omega, u, v > 0 in omega, u = v = 0 on partial differential omega where 0 < alpha < 1, 0< beta <1, 2- alpha -beta < q < N(p-1) N-p < p < r < p*, with p* = NpN-p. We will guarantee the existence of a solution in the Nehari manifold. Further by using the Lusternik-Schnirelman category we will prove the existence of at least cat(omega) + 1 number of solutions.

引用

页码：127 / 154

页数：28

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