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Quasilinear Schrödinger Equations with Asymptotically Linear Nonlinearities

2014; De Gruyter; Volume: 14; Issue: 3 Linguagem: Inglês

10.1515/ans-2014-0309

2169-0375

Marcelo F. Furtado, Edcarlos D. Silva, Maxwell L. Silva,

Numerical methods in inverse problems

Abstract We deal with the existence of nonzero solution for the quasilinear Schrödinger equation −Δu + V(x)u − Δ(u 2 )u = g(x, u), x ∈ ℝ N , u ∈ H 1 (ℝ N ), where V is a positive potential and the nonlinearity g(x, s) behaves like K 0 (x)s at the origin and like K ∞ (x)|s| p , 1 ≤ p ≤ 3, at infinity. In the proofs we apply minimization methods.