| Abstrakt: |
The main purpose of this paper is to show the existence of weak solutions for a problem involving the fractional p (x , ⋅) {p(x,\cdot\,)} -Laplacian operator of the following form: { (- Δ p (x , ⋅) ) s u (x) + w (x) | u | p ¯ (x) - 2 u = λ f (x , u) in Ω , u = 0 in ℝ N ∖ Ω , \left\{\begin{aligned} \displaystyle(-\Delta_{p(x,\cdot\,)})^{s}u(x)+w(x)% \lvert u\rvert^{\bar{p}(x)-2}u&\displaystyle=\lambda f(x,u)&&\displaystyle% \phantom{}\text{in }\Omega,\\ \displaystyle u&\displaystyle=0&&\displaystyle\phantom{}\text{in }\mathbb{R}^{% N}\setminus\Omega,\end{aligned}\right. The main tool used for this purpose is the Berkovits topological degree. [ABSTRACT FROM AUTHOR] |
