Variable s(·)-order Kirchhoff-type problem with a p(·)-fractional Laplace operator

چکیده مقاله

This paper deals with the existence and multiplicity of weak solutions for the following Kirchhoff-type problem (Formula presented.) where (Formula presented.) models a Kirchhoff coefficient and (Formula presented.) is a variable (Formula presented.) -order (Formula presented.) -fractional Laplace operator, with (Formula presented.) and (Formula presented.). Here, (Formula presented.) is a bounded smooth domain with (Formula presented.) for any (Formula presented.). By using the mountain pass theorem of Ambrosetti and Rabinowitz and Ekeland's variational principle in two cases when the Carathéodory function (Formula presented.) having special structure, we establish conditions ensuring the multiplicity results. © 2023 John Wiley & Sons, Ltd.