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Volume 6, Issue 1
Existence of Three Weak Solutions for a Class of Quasi-Linear Elliptic Operators with a Mixed Boundary Value Problem Containing $p(·)$-Laplacian in a Variable Exponent Sobolev Space

Junichi Aramaki

DOI: 10.12150/jnma.2024.107

J. Nonl. Mod. Anal., 6 (2024), pp. 107-132.

Published online: 2024-03

[An open-access article; the PDF is free to any online user.]

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  • Abstract

In this paper, we consider a mixed boundary value problem to a class of nonlinear operators containing $p(·)$-Laplacian. More precisely, we are concerned with the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary. We show the existence of at least three weak solutions under some hypotheses on given functions and the values of parameters.

  • Keywords

$p(·)$-Laplacian type equation, three weak solutions, mixed boundary value problem.

  • AMS Subject Headings

35H30, 35D05, 35J60, 35J70

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-6-107, author = {Aramaki , Junichi}, title = {Existence of Three Weak Solutions for a Class of Quasi-Linear Elliptic Operators with a Mixed Boundary Value Problem Containing $p(·)$-Laplacian in a Variable Exponent Sobolev Space}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2024}, volume = {6}, number = {1}, pages = {107--132}, abstract = {

In this paper, we consider a mixed boundary value problem to a class of nonlinear operators containing $p(·)$-Laplacian. More precisely, we are concerned with the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary. We show the existence of at least three weak solutions under some hypotheses on given functions and the values of parameters.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2024.107}, url = {http://global-sci.org/intro/article_detail/jnma/22969.html} }
TY - JOUR T1 - Existence of Three Weak Solutions for a Class of Quasi-Linear Elliptic Operators with a Mixed Boundary Value Problem Containing $p(·)$-Laplacian in a Variable Exponent Sobolev Space AU - Aramaki , Junichi JO - Journal of Nonlinear Modeling and Analysis VL - 1 SP - 107 EP - 132 PY - 2024 DA - 2024/03 SN - 6 DO - http://doi.org/10.12150/jnma.2024.107 UR - https://global-sci.org/intro/article_detail/jnma/22969.html KW - $p(·)$-Laplacian type equation, three weak solutions, mixed boundary value problem. AB -

In this paper, we consider a mixed boundary value problem to a class of nonlinear operators containing $p(·)$-Laplacian. More precisely, we are concerned with the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary. We show the existence of at least three weak solutions under some hypotheses on given functions and the values of parameters.

Junichi Aramaki. (2024). Existence of Three Weak Solutions for a Class of Quasi-Linear Elliptic Operators with a Mixed Boundary Value Problem Containing $p(·)$-Laplacian in a Variable Exponent Sobolev Space. Journal of Nonlinear Modeling and Analysis. 6 (1). 107-132. doi:10.12150/jnma.2024.107
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