Existence and multiplicity of solutions for a Schrödinger–Kirchhoff type equation involving the fractional $$p\left( .,.\right)$$ -Laplacian operator in $${\mathbb {R}}^{N}$$

Collectanea Mathematica - Tập 72 - Trang 129-156 - 2020
Rabil Ayazoglu1,2, Yeşim Saraç3, S. Şule Şener3, Gülizar Alisoy4
1Faculty of Education, Bayburt University, Bayburt, Turkey
2Institute of Mathematics and Mechanics of ANAS, Baku, Azerbaijan
3Faculty of Science, Ataturk University, Erzurum, Turkey
4Faculty of Science and Arts, Tekirdağ Namik Kemal University, Tekirdağ, Turkey

Tóm tắt

In this paper, by using variational approach, Mountain Pass Theorem and Krasnoselskii’s genus theory, we show the existence and multiplicity of solutions for a Schrödinger–Kirchhoff type equation involving the fractional $$p\left( .,.\right)$$ -Laplacian in fractional Sobolev space with variable exponent. We also establish a Bartsch–Wang type compact embedding theorem for fractional Sobolev space with variable exponent.

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