MULTIPLICITY RESULTS FOR CRITICAL FRACTIONAL EQUATIONS WITH SIGN-CHANGING WEIGHT FUNCTIONS

被引：0

作者：

Pu, Yang ^{[1
]}

Liao, Jia-Feng ^{[2
]}

机构：

[1] China West Normal Univ, Sch Math & Informat, Nanchong 637009, Sichuan, Peoples R China

[2] China West Normal Univ, Coll Math Educ, Nanchong 637009, Sichuan, Peoples R China

来源：

DIFFERENTIAL EQUATIONS & APPLICATIONS | 2021年 / 13卷 / 02期

关键词：

Fractional laplacian equations; variational techniques; critical growth; BREZIS-NIRENBERG RESULT; CONVEX NONLINEARITIES; NEHARI MANIFOLD; CONCAVE; BIFURCATION; REGULARITY; EXISTENCE;

D O I：

10.7153/dea-2021-13-09

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider a time-independent fractional equation: {(-Delta)su = f(x)vertical bar u vertical bar(2s*-2)u+g(x)vertical bar u vertical bar(q-1)u, x is an element of Omega; u = 0, x is an element of R-N\Omega where Omega is a smooth bounded domain, s is an element of (0,1), N > 2s, 0 < q < 1, the coefficient functions f and g may change sign. We first obtain the existence of ground state solution by the Nehari method under the combined effect of coefficient functions. Then we find the multiplicity of positive solutions by Mountain pass theorem under some stronger conditions, and one of them is a ground state solution.

引用

页码：151 / 171

页数：21

共 35 条

[1] COMBINED EFFECTS OF CONCAVE AND CONVEX NONLINEARITIES IN SOME ELLIPTIC PROBLEMS
AMBROSETTI, A
BREZIS, H
CERAMI, G
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1994, 122 (02) : 519 - 543
[2] [Anonymous], 1996, CAMB TRACTS MATH
[3] [Anonymous], 1997, Minimax theorems
[4] Applebaum D., 2009, CAMB STUD ADV MATH, V116
[5] A critical fractional equation with concave convex power nonlinearities
Barrios, B.
Colorado, E.
Servadei, R.
Soria, F.
[J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2015, 32 (04): : 875 - 900
[6] On some critical problems for the fractional Laplacian operator
Barrios, B.
Colorado, E.
de Pablo, A.
Sanchez, U.
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 252 (11) : 6133 - 6162
[7] BERESTYCKI H, 1983, ARCH RATION MECH AN, V82, P313
[8] A RELATION BETWEEN POINTWISE CONVERGENCE OF FUNCTIONS AND CONVERGENCE OF FUNCTIONALS
BREZIS, H
LIEB, E
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 88 (03) : 486 - 490
[9] Nonlinear equations for fractional Laplacians, I: Regularity, maximum principles, and Hamiltonian estimates
Cabre, Xavier
Sire, Yannick
[J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2014, 31 (01): : 23 - 53
[10] INFINITELY MANY SOLUTIONS FOR CRITICAL FRACTIONAL EQUATION WITH SIGN-CHANGING WEIGHT FUNCTION
Chen, Wei
Tang, Chun-Lei
[J]. JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2020, 10 (01): : 131 - 139

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