Artículo de revista
Intermediate reduction method and infinitely many positive solutions of nonlinear Schrödinger equations with non-symmetric potentials
Fecha
2015Registro en:
Calc. Var. (2015) 53:473–523
0944-2669
DOI: 10.1007/s00526-014-0756-3
Autor
Pino Manresa, Manuel del
Wei, Juncheng
Yao, Wei
Institución
Resumen
We consider the standing-wave problem for a nonlinear Schrödinger equation,
corresponding to the semilinear elliptic problem
− u + V(x)u = |u|p−1u, u ∈ H1(R2),
where V(x) is a uniformly positive potential and p > 1. Assuming that
V(x) = V∞ + a
|x|m
+ O
1
|x|m+σ
, as |x| → +∞,
for instance if p > 2, m > 2 andσ > 1 we prove the existence of infinitely many positive
solutions. If V(x) is radially symmetric, this result was proved in [43]. The proof without
symmetries is much more difficult, and for that we develop a new intermediate Lyapunov–
Schmidt reductionmethod,which is a compromise between the finite and infinite dimensional
versions of it.