Localized concentration of semiclassical solutions for double phase problems with nonlocal reaction

Localized concentration of semiclassical solutions for double phase problems with nonlocal reaction

Článek WoS

This paper focuses on the study of multiplicity and localized concentration properties of positive solutions for the following singularly perturbed double phase problem with nonlocal Choquard reaction {-epsilon(p)Delta(p)u - epsilon(q)Delta(q)u + V(x)(|u|(p-2)u + |u|(q-2)u) = epsilon(& micro;-N) ( 1 / |x|(& micro;) * G(u)) g(u), in R-N, u is an element of W-1,W-p(R-N) boolean AND W-1,W-q(R-N), u > 0, in R-N, where 1 < p < q < N, 0 < & micro; < p, epsilon is a small positive parameter and V is the absorption potential. We assume that the potential V satisfies only a local condition introduced by del Pino and Felmer. Applying suitable variational and topological methods combined with penalization technique, we obtain multiple semiclassical positive solutions for epsilon > 0 sufficiently small as well as related concentration properties, in relationship with the set where the potential V attains its minimum. Moreover, we also investigate the decay property of semiclassical positive solutions. The main results included in this paper complement several recent contributions to the study of concentration phenomena.

This paper focuses on the study of multiplicity and localized concentration properties of positive solutions for the following singularly perturbed double phase problem with nonlocal Choquard reaction {-epsilon(p)Delta(p)u - epsilon(q)Delta(q)u + V(x)(|u|(p-2)u + |u|(q-2)u) = epsilon(& micro;-N) ( 1 / |x|(& micro;) * G(u)) g(u), in R-N, u is an element of W-1,W-p(R-N) boolean AND W-1,W-q(R-N), u > 0, in R-N, where 1 < p < q < N, 0 < & micro; < p, epsilon is a small positive parameter and V is the absorption potential. We assume that the potential V satisfies only a local condition introduced by del Pino and Felmer. Applying suitable variational and topological methods combined with penalization technique, we obtain multiple semiclassical positive solutions for epsilon > 0 sufficiently small as well as related concentration properties, in relationship with the set where the potential V attains its minimum. Moreover, we also investigate the decay property of semiclassical positive solutions. The main results included in this paper complement several recent contributions to the study of concentration phenomena.

Double phase problem; Semiclassical solution; Localized concentration; Nonlocal reaction

Double phase problem; Semiclassical solution; Localized concentration; Nonlocal reaction

RADULESCU, V.; ZHANG, J.; ZHANG, W.

2026

18.03.2026

Analysis and mathematical physics

16

2

Švýcarská konfederace

54

https://link.springer.com/article/10.1007/s13324-026-01182-x?utm_source=getftr&utm_medium=getftr&utm_campaign=getftr_pilot&getft_integrator=clarivate