Publikationsdatum:
2015-09-12
Beschreibung:
In this paper, we study the following linearly coupled system − ε 2 Δ u i + P i ( x ) u i = u i 3 + ∑ j ≠ i N λ i j u j , u i ∈ H 1 ( R 3 ) , i = 1 , … , N , where ε 〉 0 is a small parameter, P i ( x ) are positive potentials, and λ ij = λ ji 〉 0 ( i ≠ j ) are coupling constants for i , j = 1, …, N . We investigate the effect of potentials to the structure of the solutions. More precisely, we construct multi-spikes solutions concentrating near the local maximum point x 0 i of P i ( x ). When x 0 i = x 0 j , P i ( x 0 i ) = P j ( x 0 j ) = a , i ≠ j , i , j = 1 , … , N , the components have spikes clustering at the same point as ε → 0 + . When x 0 i ≠ x 0 j , i ≠ j , the components have spikes clustering at the different points as ε → 0 + .
Print ISSN:
0022-2488
Digitale ISSN:
1089-7658
Thema:
Mathematik
,
Physik
Permalink
