Publication result detail

Multiplicity of solutions for nonlinear coercive problems

DIBLÍK, J.; GALEWSKI, M.; RADULESCU, V.; ŠMARDA, Z.

Original Title

Multiplicity of solutions for nonlinear coercive problems

English Title

Multiplicity of solutions for nonlinear coercive problems

Type

WoS Article

Original Abstract

We are concerned in this paper with problems that involve nonlinear potential mappings satisfying condition (S) and whose potentials are coercive. We first provide mild sufficient conditions for the minimizing sequence in the Weierstrass-Tonelli theorem in order to have strongly convergent subsequences. Next, we establish a three critical point theorem which is based on the Pucci-Serrin type mountain pass lemma and which is an infinite dimensional counterpart of the Courant theorem. Ricceri-type three critical point results then follow. Some applications to Dirichlet boundary value problems driven by the perturbed Laplacian are given in the final part of this paper.

English abstract

We are concerned in this paper with problems that involve nonlinear potential mappings satisfying condition (S) and whose potentials are coercive. We first provide mild sufficient conditions for the minimizing sequence in the Weierstrass-Tonelli theorem in order to have strongly convergent subsequences. Next, we establish a three critical point theorem which is based on the Pucci-Serrin type mountain pass lemma and which is an infinite dimensional counterpart of the Courant theorem. Ricceri-type three critical point results then follow. Some applications to Dirichlet boundary value problems driven by the perturbed Laplacian are given in the final part of this paper.

Keywords

Coercive functional;Multiple solutions; Nonlinear equations

Key words in English

Coercive functional;Multiple solutions; Nonlinear equations

Authors

DIBLÍK, J.; GALEWSKI, M.; RADULESCU, V.; ŠMARDA, Z.

RIV year

2024

Released

01.12.2023

Publisher

Elsevier

ISBN

0022-247X

Periodical

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Volume

528

Number

1

State

United States of America

Pages from

1

Pages to

13

Pages count

13

URL

https://www.sciencedirect.com/science/article/pii/S0022247X23004766

Full text in the Digital Library

http://hdl.handle.net/11012/245180

BibTex

@article{BUT185038,
  author="Josef {Diblík} and Marek {Galewski} and Vicentiu {Radulescu} and Zdeněk {Šmarda}",
  title="Multiplicity of solutions for nonlinear coercive problems",
  journal="JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS",
  year="2023",
  volume="528",
  number="1",
  pages="1--13",
  doi="10.1016/j.jmaa.2023.127473",
  issn="0022-247X",
  url="https://www.sciencedirect.com/science/article/pii/S0022247X23004766"
}

Documents

1-s2.0-S0022247X23004766-main