Existence of solutions for a system of coupled nonlinear stationary bi-harmonic Schrödinger equations

P. Álvarez-Caudevilla, E. Colorado, V. A. Galaktionov

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)78-93
Number of pages16
JournalNonlinear Analysis: Real World Applications
Volume23
Early online date18 Dec 2014
DOIs
Publication statusPublished - Jun 2015

Fingerprint

Biharmonic Equation
Semilinear
Schrödinger Equation
Existence of Solutions
Critical point
Nehari Manifold
Mountain Pass Theorem
Infinitely Many Solutions
Biharmonic
Multiplicity Results
Schrödinger
Existence Results
Countable
Existence of solutions
Class
Family
Multiplicity

Keywords

  • Critical point theory
  • equations
  • Nonlinear bi-harmonic Schrödinger
  • Standing waves

Cite this

Existence of solutions for a system of coupled nonlinear stationary bi-harmonic Schrödinger equations. / Álvarez-Caudevilla, P.; Colorado, E.; Galaktionov, V. A.

In: Nonlinear Analysis: Real World Applications, Vol. 23, 06.2015, p. 78-93.

Research output: Contribution to journalArticle

@article{e92b10cebbab4cb9944d2943d051f645,
title = "Existence of solutions for a system of coupled nonlinear stationary bi-harmonic Schr{\"o}dinger equations",
abstract = "We obtain existence and multiplicity results for the solutions of a class of coupled semilinear bi-harmonic Schr{\"o}dinger 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 Schr{\"o}dinger system under study in this work.",
keywords = "Critical point theory, equations, Nonlinear bi-harmonic Schr{\"o}dinger, Standing waves",
author = "P. {\'A}lvarez-Caudevilla and E. Colorado and Galaktionov, {V. A.}",
year = "2015",
month = "6",
doi = "10.1016/j.nonrwa.2014.11.009",
language = "English",
volume = "23",
pages = "78--93",
journal = "Nonlinear Analysis: Real World Applications",
issn = "1468-1218",
publisher = "Elsevier",

}

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

VL - 23

SP - 78

EP - 93

JO - Nonlinear Analysis: Real World Applications

JF - Nonlinear Analysis: Real World Applications

SN - 1468-1218

ER -