Variable order nonlocal Choquard problem with variable exponents

被引:35
作者
Biswas, Reshmi [1 ]
Tiwari, Sweta [1 ]
机构
[1] Indian Inst Technol Guwahati, Dept Math, Gauhati, Assam, India
关键词
Choquard problem; Hardy-Sobolev-Littlewood inequality; Variable order fractional p(.)- Laplacian; concave-convex nonlinearities; MULTIPLICITY; EXISTENCE; EQUATIONS; CONCAVE; SPACES; GUIDE;
D O I
10.1080/17476933.2020.1751136
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this article, we study the existence/multiplicity results for the variable order nonlocal Choquard problem with variable exponents (-Delta)(p(.))(s(.))u(x) = lambda vertical bar u(x)vertical bar(alpha(x)-2u)(x) +(integral(Omega) F(y, u(y))/vertical bar x - y vertical bar(u(x,y)) dy) f(x, u(x)), x is an element of Omega, u(x) = 0, x is an element of Omega(epsilon) := R-N\Omega, where Omega subset of R-N is a smooth and bounded domain, N >= 2, p, s, mu and alpha are continuous functions on R-N x R-N and f(x, t) is a Caratheodory function with F(x, t) := integral(t)(0) f(x, s) ds. Under suitable assumption on s, p, mu, alpha and f(x, t), first we study the analogous Hardy-Sobolev-Littlewood-type result for variable exponents suitable for the fractional Sobolev space with variable order and variable exponents. Then we give the existence/multiplicity results for the above equation.
引用
收藏
页码:853 / 875
页数:23
相关论文
共 36 条
[1]   A Hardy-Littlewood-Sobolev-Type Inequality for Variable Exponents and Applications to Quasilinear Choquard Equations Involving Variable Exponent [J].
Alves, Claudianor O. ;
Tavares, Leandro S. .
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2019, 16 (02)
[2]   Generalized Choquard Equations Driven by Nonhomogeneous Operators [J].
Alves, Claudianor O. ;
Radulescu, Vicentiu D. ;
Tavares, Leandro S. .
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2019, 16 (01)
[3]   COMBINED EFFECTS OF CONCAVE AND CONVEX NONLINEARITIES IN SOME ELLIPTIC PROBLEMS [J].
AMBROSETTI, A ;
BREZIS, H ;
CERAMI, G .
JOURNAL OF FUNCTIONAL ANALYSIS, 1994, 122 (02) :519-543
[4]  
[Anonymous], 2016, ELECT J DIFFERENTIAL
[5]  
[Anonymous], 2001, ANALYSIS-UK
[6]   ON A NEW FRACTIONAL SOBOLEV SPACE AND APPLICATIONS TO NONLOCAL VARIATIONAL PROBLEMS WITH VARIABLE EXPONENT [J].
Bahrouni, Anouar ;
Radulescu, Vicentiu D. .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2018, 11 (03) :379-389
[7]   Comparison and sub-supersolution principles for the fractional p(x)-Laplacian [J].
Bahrouni, Anouar .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 458 (02) :1363-1372
[8]   A critical fractional equation with concave convex power nonlinearities [J].
Barrios, B. ;
Colorado, E. ;
Servadei, R. ;
Soria, F. .
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2015, 32 (04) :875-900
[9]  
Bisci GM, 2016, ENCYCLOP MATH APPL, V162
[10]   Multiplicity results for elliptic fractional equations with subcritical term [J].
Bisci, Giovanni Molica ;
Radulescu, Vicentiu D. .
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2015, 22 (04) :721-739