On a p(x)-Kirchhoff-type Equation with Singular and Superlinear Nonlinearities

Mustafa Avci

doi:10.1007/s12591-024-00702-0

On a p(x)-Kirchhoff-type Equation with Singular and Superlinear Nonlinearities

Mustafa Avci

Centre for Science

Research output: Contribution to journal › Journal Article › peer-review

5 Citations (Scopus)

Abstract

In the present paper, we study a p(x)-Kirchhoff-type equation with combined effects of variable singular and superlinear nonlinearities. Using the Ekeland’s variational principle and a constrained minimization approach, we show the existence and uniqueness of a positive solution for the case variable singularity β(x) assumes its values in the interval (1,∞), i.e., the case where β(x) causes a strong singularity.

Original language	English
Pages (from-to)	673-695
Number of pages	23
Journal	Differential Equations and Dynamical Systems
Volume	34
Issue number	3
DOIs	https://doi.org/10.1007/s12591-024-00702-0
Publication status	Published - Jul 2026

Keywords

35A15
35A21
35J65
35J75
Constrained minimization
Ekeland’s variational principle
Strong Singularity
Superlinear nonlinearity
p(x)-Kirchhoff equation

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10.1007/s12591-024-00702-0

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title = "On a p(x)-Kirchhoff-type Equation with Singular and Superlinear Nonlinearities",

abstract = "In the present paper, we study a p(x)-Kirchhoff-type equation with combined effects of variable singular and superlinear nonlinearities. Using the Ekeland{\textquoteright}s variational principle and a constrained minimization approach, we show the existence and uniqueness of a positive solution for the case variable singularity β(x) assumes its values in the interval (1,∞), i.e., the case where β(x) causes a strong singularity.",

keywords = "35A15, 35A21, 35J65, 35J75, Constrained minimization, Ekeland{\textquoteright}s variational principle, Strong Singularity, Superlinear nonlinearity, p(x)-Kirchhoff equation",

author = "Mustafa Avci",

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year = "2026",

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language = "English",

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T1 - On a p(x)-Kirchhoff-type Equation with Singular and Superlinear Nonlinearities

AU - Avci, Mustafa

N1 - Publisher Copyright: © Foundation for Scientific Research and Technological Innovation 2024.

PY - 2026/7

Y1 - 2026/7

N2 - In the present paper, we study a p(x)-Kirchhoff-type equation with combined effects of variable singular and superlinear nonlinearities. Using the Ekeland’s variational principle and a constrained minimization approach, we show the existence and uniqueness of a positive solution for the case variable singularity β(x) assumes its values in the interval (1,∞), i.e., the case where β(x) causes a strong singularity.

AB - In the present paper, we study a p(x)-Kirchhoff-type equation with combined effects of variable singular and superlinear nonlinearities. Using the Ekeland’s variational principle and a constrained minimization approach, we show the existence and uniqueness of a positive solution for the case variable singularity β(x) assumes its values in the interval (1,∞), i.e., the case where β(x) causes a strong singularity.

KW - 35A15

KW - 35A21

KW - 35J65

KW - 35J75

KW - Constrained minimization

KW - Ekeland’s variational principle

KW - Strong Singularity

KW - Superlinear nonlinearity

KW - p(x)-Kirchhoff equation

UR - https://www.scopus.com/pages/publications/85204743765

U2 - 10.1007/s12591-024-00702-0

DO - 10.1007/s12591-024-00702-0

M3 - Journal Article

AN - SCOPUS:85204743765

SN - 0971-3514

VL - 34

SP - 673

EP - 695

JO - Differential Equations and Dynamical Systems

JF - Differential Equations and Dynamical Systems

IS - 3

ER -

On a p(x)-Kirchhoff-type Equation with Singular and Superlinear Nonlinearities

Abstract

Keywords

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