Journal
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
Volume 63, Issue 2, Pages 233-248Publisher
SPRINGER BASEL AG
DOI: 10.1007/s00033-011-0166-8
Keywords
Nonlinear Choquard equation; Nonlocal nonlinearity; Electromagnetic potential; Multiple solutions; Intertwining solutions
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Funding
- MIUR
- CONACYT [129847]
- PAPIIT (Mexico) [IN101209]
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We consider the stationary nonlinear magnetic Choquard equation (-i del + A(x))(2)u + V(x)u = (1/|x|(alpha) * |u|(p-2)u, x is an element of R-N where A is a real-valued vector potential, V is a real-valued scalar potential, N >= 3, alpha is an element of (0, N) and 2 - (alpha/N) < p < (2N - alpha)/(N - 2). We assume that both A and V are compatible with the action of some group G of linear isometries of RN. We establish the existence of multiple complex valued solutions to this equation which satisfy the symmetry condition. u(gx) = tau(g)u(x) for all g is an element of G, x is an element of R-N, where tau : G -> S-1 is a given group homomorphism into the unit complex numbers.
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