Work

Solutions for fractional $p(x,\cdot )$-Kirchhoff-type equations in $\mathbb{R}^{N}$

Year: 2024

Type: article

Abstract: In this paper, we discuss the fractional $p(x,\cdot )$ -Kirchhoff-type equations $$ M\left (\int _{\mathbb{R}^{N}\times \mathbb{R}^{N}} \frac{1}{p(x,y)} \frac{|u(x)-u(y)|^{p(x,y)}}{|x-y|^{N+sp(x,y)}}dxdy\right )(-\Delta _{p(x,.)})^{s} u+|u|^{\bar{p}(x)-2}u=f(x,u).$$ We weaken the conditions on the nonlinear term f and get the existence and multiplicity of solutions via variational methods, which improves some previous results.

Source: Journal of Inequalities and Applications

DOI: 10.1186/s13660-024-03204-3

Author: Lili Wan

Institution: Southwest University of Science and Technology

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,990

OpenAlex ID: W4402648564