Existence and multiplicity results for a nonlinear stationary Schrödinger equation

Danila Sandra Moschetto. "Existence and multiplicity results for a nonlinear stationary Schrödinger equation." Annales Polonici Mathematici 99.1 (2010): 39-43. <http://eudml.org/doc/280371>.

@article{DanilaSandraMoschetto2010,
abstract = {We revisit Kristály’s result on the existence of weak solutions of the Schrödinger equation of the form -Δu + a(x)u = λb(x)f(u), $x ∈ ℝ^N$, $u ∈ H¹(ℝ^N)$, where λ is a positive parameter, a and b are positive functions, while $f:ℝ → ℝ$ is sublinear at infinity and superlinear at the origin. In particular, by using Ricceri’s recent three critical points theorem, we show that, under the same hypotheses, a much more precise conclusion can be obtained.},
author = {Danila Sandra Moschetto},
journal = {Annales Polonici Mathematici},
keywords = {nonlinear stationary Schrödinger equations; multiple solutions},
language = {eng},
number = {1},
pages = {39-43},
title = {Existence and multiplicity results for a nonlinear stationary Schrödinger equation},
url = {http://eudml.org/doc/280371},
volume = {99},
year = {2010},
}

TY - JOUR
AU - Danila Sandra Moschetto
TI - Existence and multiplicity results for a nonlinear stationary Schrödinger equation
JO - Annales Polonici Mathematici
PY - 2010
VL - 99
IS - 1
SP - 39
EP - 43
AB - We revisit Kristály’s result on the existence of weak solutions of the Schrödinger equation of the form -Δu + a(x)u = λb(x)f(u), $x ∈ ℝ^N$, $u ∈ H¹(ℝ^N)$, where λ is a positive parameter, a and b are positive functions, while $f:ℝ → ℝ$ is sublinear at infinity and superlinear at the origin. In particular, by using Ricceri’s recent three critical points theorem, we show that, under the same hypotheses, a much more precise conclusion can be obtained.
LA - eng
KW - nonlinear stationary Schrödinger equations; multiple solutions
UR - http://eudml.org/doc/280371
ER -