Existence and multiplicity of solutions for a singular problem involving the p-biharmonic operator in RN

被引：7

作者：

Dhifli, Abdelwaheb ^{[1
,2
]}

Alsaedi, Ramzi ^{[3
]}

机构：

[1] Univ Jeddah, Dept Math, Fac Sci, Jeddah, Saudi Arabia

[2] Univ Tunis El Manar, Inst Preparatoire Etud Ingenieurs Manar, LR10ES09 Modelisat Math Anal Harmon & Theorie Pot, Tunis 2092, Tunisia

[3] King Abdulaziz Univ, Fac Sci, Dept Math, POB 80203, Jeddah 21589, Saudi Arabia

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2021年 / 499卷 / 02期

关键词：

p-Biharmonic equations; Existence result; Multiple solutions; Nehari manifold; Fibering maps;

D O I：

10.1016/j.jmaa.2021.125049

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we are interested in the existence and the multiplicity of solutions for the following singular p-biharmonic problem with Rellich potential Delta(2)(p)u - mu vertical bar u vertical bar(p-2)u/vertical bar x vertical bar(2p) - Delta(p)u = lambda f(x)u(q-1) + g(x)u(m-1), in R-N u(x) > 0, in R-N where 1 < p < N/2, 0 < m < 1, p < q < pN/N - 2p, lambda is a positive real parameter and 0 < mu < gamma(N,p) with gamma(N,p) = (N(p-1) (N-2p)/p(2))(p). Under some appropriate assumptions on the functions f and g, by using the Nehari manifold combined with the fibering maps, we obtain the existence of two positive entire solutions. (C) 2021 Published by Elsevier Inc.

引用

页数：19

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