TY - JOUR
T1 - Existence of solutions for a system of coupled nonlinear stationary bi-harmonic Schrödinger equations
AU - Álvarez-Caudevilla, P.
AU - Colorado, E.
AU - Galaktionov, V. A.
PY - 2015/6
Y1 - 2015/6
N2 - We obtain existence and multiplicity results for the solutions of a class of coupled semilinear bi-harmonic Schrödinger equations. Actually, using the classical Mountain Pass Theorem and minimization techniques, we prove the existence of critical points of the associated functional constrained on the Nehari manifold. Furthermore, we show that using the so-called fibering method and the Lusternik-Schnirel'man theory there exist infinitely many solutions, actually a countable family of critical points, for such a semilinear bi-harmonic Schrödinger system under study in this work.
AB - We obtain existence and multiplicity results for the solutions of a class of coupled semilinear bi-harmonic Schrödinger equations. Actually, using the classical Mountain Pass Theorem and minimization techniques, we prove the existence of critical points of the associated functional constrained on the Nehari manifold. Furthermore, we show that using the so-called fibering method and the Lusternik-Schnirel'man theory there exist infinitely many solutions, actually a countable family of critical points, for such a semilinear bi-harmonic Schrödinger system under study in this work.
KW - Critical point theory
KW - equations
KW - Nonlinear bi-harmonic Schrödinger
KW - Standing waves
UR - http://www.scopus.com/inward/record.url?scp=84919615395&partnerID=8YFLogxK
UR - http://dx.doi.org/10.1016/j.nonrwa.2014.11.009
U2 - 10.1016/j.nonrwa.2014.11.009
DO - 10.1016/j.nonrwa.2014.11.009
M3 - Article
AN - SCOPUS:84919615395
SN - 1468-1218
VL - 23
SP - 78
EP - 93
JO - Nonlinear Analysis: Real World Applications
JF - Nonlinear Analysis: Real World Applications
ER -