| Full text | |
| Author(s): |
Carlos, Romulo D.
;
de Oliveira, Victor C.
;
Miyagaki, Olimpio H.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | Electronic Journal of Qualitative Theory of Differential Equations; v. N/A, n. 2, p. 32-pg., 2025-01-01. |
| Abstract | |
This paper is concerned with the existence and multiplicity of a ground state solution for the following class of elliptic fractional type problems given by {(-Delta)(s)(p)u+|u|(p-2)u=lambda h(1)(x)|u|(theta-2)u ln|u|+q/q+r b(1)(x)|v|(R)|u|(q-2)u in Omega, (-Delta)(t)(p)v+|v|(p-2)v=mu h(2)(x)|v|(theta-2)v ln|v|+r/q+r b(2)(x)|u|(R)|v|(q-2)v in Omega, u=v=0, in R-N\Omega, where Omega subset of RN Omega subset of RN is a bounded domain with Lipschitz boundary, s,t is an element of (0,1)s,t is an element of(0,1), N>max {ps,pt}, lambda,mu>0 lambda,mu>0, p <=theta p <=theta, 2<q+r <min {p(N)/N-ps, p(N)/N-pt}, and the additional weights h(1),h(2),b(1),b(2)is an element of C(Omega(-))are such that: b(1)(x),b(2)(x) are positive functions and h(1)(x),h(2)(x) are sign-changing functions. The operators (-Delta)(s)(p) and (-Delta)(t)(p) represents, both, fractional p- Laplacian operator, a generalization for the fractional Laplacian (-Delta)(s),0<s<1(p=2), defined in a integral way as (-Delta)(s)u(x):=c(n,s)/2 integral(N)(R)2u(x)-(x+y)-u(x-y)/|y|(n+2s)dy, x is an element of R-N, where c(n,s) is a positive normalizing constant, and another fractional operator. Specifically, the operators (-Delta)(s)(p) and(-Delta)(t)(p) are defined, up to a normalization constant, by the formula (-Delta)(l)(p)u(x):=lim 2(epsilon -> 0+)integral(N)(R)\B epsilon(x)|u(x)-u(y)|(p-2)(u(x)-u(y))/|x-y|(N+sp) dy, for all u is an element of C-0(infinity)(R-N),x is an element of R-N, and l is an element of{s,t}. (AU) | |
| FAPESP's process: | 22/16407-1 - TESdE: Thematic on Equations and Systems of differential Equations |
| Grantee: | Ederson Moreira dos Santos |
| Support Opportunities: | Research Projects - Thematic Grants |