Publication result detail

Existence results for non-coercive problems

DIBLÍK, J.; GALEWSKI, M.; ŠMARDA, Z.

Original Title

Existence results for non-coercive problems

English Title

Existence results for non-coercive problems

Type

WoS Article

Original Abstract

In this article, we investigate non-coercive variational equations under assumptions related to generalized monotonicity. We present some general abstract tools regarding the existence of bounded solutions and their multiplicity, which we then apply to the Dirichlet boundary value problem driven by the perturbed (negative) p p -Laplacian. As a by-product of our findings, we provide a version of the Browder-Minty theorem in the potential case that does not involve the Brouwer fixed-point theorem but utilizes optimization techniques.

English abstract

In this article, we investigate non-coercive variational equations under assumptions related to generalized monotonicity. We present some general abstract tools regarding the existence of bounded solutions and their multiplicity, which we then apply to the Dirichlet boundary value problem driven by the perturbed (negative) p p -Laplacian. As a by-product of our findings, we provide a version of the Browder-Minty theorem in the potential case that does not involve the Brouwer fixed-point theorem but utilizes optimization techniques.

Keywords

Dirichlet problem; Minty-Browder theorem; multiple solutions; non-coercive problem; p-Laplacian

Key words in English

Dirichlet problem; Minty-Browder theorem; multiple solutions; non-coercive problem; p-Laplacian

Authors

DIBLÍK, J.; GALEWSKI, M.; ŠMARDA, Z.

Released

01.01.2025

Publisher

De Gruyter

ISBN

2191-950X

Periodical

Advances in Nonlinear Analysis

Volume

14

Number

1

State

Federal Republic of Germany

Pages from

1

Pages to

13

Pages count

13

URL

https://www.degruyterbrill.com/document/doi/10.1515/anona-2025-0071/html

Full text in the Digital Library

http://hdl.handle.net/11012/255367

BibTex

@article{BUT198252,
  author="Josef {Diblík} and Marek {Galewski} and Zdeněk {Šmarda}",
  title="Existence results for non-coercive problems",
  journal="Advances in Nonlinear Analysis",
  year="2025",
  volume="14",
  number="1",
  pages="1--13",
  doi="10.1515/anona-2025-0071",
  issn="2191-9496",
  url="https://www.degruyterbrill.com/document/doi/10.1515/anona-2025-0071/html"
}

Documents

10.1515_anona-2025-0071