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Volume 39, Issue 4
Kirchhoff-Type Problem with Mixed Boundary Condition in a Variable Exponent Sobolev Space

Junichi Aramaki

DOI: 10.4208/cmr.2023-0017

Commun. Math. Res., 39 (2023), pp. 539-574.

Published online: 2023-11

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  • Abstract

In this paper, we consider a mixed boundary value problem for the stationary Kirchhoff-type equation 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 one, two or infinitely many nontrivial weak solutions according to hypotheses on given functions.

  • Keywords

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

  • AMS Subject Headings

35H30, 35D05, 35J60, 35J70

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-39-539, author = {Aramaki , Junichi}, title = {Kirchhoff-Type Problem with Mixed Boundary Condition in a Variable Exponent Sobolev Space}, journal = {Communications in Mathematical Research }, year = {2023}, volume = {39}, number = {4}, pages = {539--574}, abstract = {

In this paper, we consider a mixed boundary value problem for the stationary Kirchhoff-type equation 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 one, two or infinitely many nontrivial weak solutions according to hypotheses on given functions.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2023-0017}, url = {http://global-sci.org/intro/article_detail/cmr/22100.html} }
TY - JOUR T1 - Kirchhoff-Type Problem with Mixed Boundary Condition in a Variable Exponent Sobolev Space AU - Aramaki , Junichi JO - Communications in Mathematical Research VL - 4 SP - 539 EP - 574 PY - 2023 DA - 2023/11 SN - 39 DO - http://doi.org/10.4208/cmr.2023-0017 UR - https://global-sci.org/intro/article_detail/cmr/22100.html KW - Kirchhoff-type problem, mixed boundary value problem, $p(·)$-Laplacian type equation, weak solutions. AB -

In this paper, we consider a mixed boundary value problem for the stationary Kirchhoff-type equation 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 one, two or infinitely many nontrivial weak solutions according to hypotheses on given functions.

Junichi Aramaki. (2023). Kirchhoff-Type Problem with Mixed Boundary Condition in a Variable Exponent Sobolev Space. Communications in Mathematical Research . 39 (4). 539-574. doi:10.4208/cmr.2023-0017
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