Entire solutions for a class of variational problems involving the biharmonic operator and Rellich potentials

被引：35

作者：

Bhakta, Mousomi ^{[2
]}

Musina, Roberta ^{[1
]}

机构：

[1] Univ Udine, Dipartimento Matemat & Informat, I-33100 Udine, Italy

[2] TIFR Ctr Applicable Math, Bangalore 560065, Karnataka, India

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2012年 / 75卷 / 09期

关键词：

Caffarelli-Kohn-Nirenberg type inequalities; Weighted biharmonic operator; Dilation invariance; Breaking symmetry; INEQUALITIES; EQUATIONS; SYMMETRY;

D O I：

10.1016/j.na.2012.02.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study existence, multiplicity and qualitative properties of entire solutions for a noncompact problem related to second-order interpolation inequalities with weights. More precisely, we deal with the following family of equationsis Delta(2)u =lambda vertical bar x vertical bar(-4)u + vertical bar x vertical bar(-beta)vertical bar u vertical bar(q-2)u in R-N, where N >= 5,q > 2,beta = N - q( N - 4)/2 and lambda is an element of R is smaller than the Rellich constant. (C) 2012 Elsevier Ltd. All rights reserved.

引用

页码：3836 / 3848

页数：13

共 35 条

[21] NONTRIVIAL SOLUTIONS FOR KIRCHHOFF-TYPE PROBLEMS INVOLVING THE p(x)-LAPLACE OPERATOR [J].

Ghanmi, Abdeljabbar .

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2018, 48 (04) :1145-1158

[22] EXISTENCE OF POSITIVE SOLUTIONS FOR BREZIS-NIRENBERG TYPE PROBLEMS INVOLVING AN INVERSE OPERATOR [J].

Alvarez-Caudevilla, Pablo ;

Colorado, Eduardo ;

Ortega, Alejandro .

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2021,

[23] EXISTENCE, NONEXISTENCE, AND DEGENERACY OF LIMIT SOLUTIONS TO p-LAPLACE PROBLEMS INVOLVING HARDY POTENTIALS AS p → 1 + [J].

Chata, Juan carlos ortiz ;

Petitta, Francesco .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2024, 56 (06) :7014-7042

[24] Multiple Solutions for a Non-cooperative Elliptic System of Kirchhoff Type Involving p-Biharmonic Operator and Critical Growth [J].

Nguyen Thanh Chung .

ACTA APPLICANDAE MATHEMATICAE, 2020, 165 (01) :1-17

[25] Solutions for a class of problems driven by an anisotropic (p, q)-Laplacian type operator [J].

Tavares, Leandro .

COMMUNICATIONS IN ANALYSIS AND MECHANICS, 2023, 15 (03) :533-550

[26] Multiplicity of weak solutions for a class of quasilinear elliptic Neumann problems using Variational methods [J].

Ahmed, Ahmed ;

Vall, Mohamed Saad Bouh E. L. E. M. I. N. E. .

BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, 2025, 43

[27] Multiple solutions for a class of nonlinear elliptic problems with a p-Laplacian type operator [J].

Huang, Yisheng ;

Zhou, Yuying .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (7-8) :3388-3395

[28] Ground state solutions for a class of elliptic Dirichlet problems involving the p(x)-Laplacian [J].

Ge, Bin ;

Zhuge, Xiang-Wu ;

Yuan, Wen-Shuo .

ANALYSIS AND MATHEMATICAL PHYSICS, 2021, 11 (03)

[29] Existence of Solutions for a Class of Dirichlet Problems Involving Fractional (p, q)-Laplacian Operators [J].

Moujani, Hasna ;

El Mfadel, Ali ;

Kassidi, Abderrazak ;

Elomari, M'hamed .

JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, 2024, 30 (04)

[30] Multiple positive solutions for a class of concave-convex elliptic problems in RN involving sign-changing weight [J].

Wu, Tsung-fang .

JOURNAL OF FUNCTIONAL ANALYSIS, 2010, 258 (01) :99-131

← 1 2 3 4 →