Sign-changing solutions for Kirchhoff-type problems involving variable-order fractional Laplacian and critical exponents

TL;DR: This paper investigates Kirchhoff-type variable-order fractional Laplacian problems with critical exponents and logarithmic nonlinearity, establishing the existence of a least energy sign-changing solution with energy strictly larger than twice the ground energy.

TL;DR: In this paper , the existence of the least energy sign-changing solution for the following degenerate Kirchhoff-type problem involving the fractional N/s-Laplacian with logarithmic and both subcritical and critical exponential nonlinearities was studied.

TL;DR: In this paper, a framework for function spaces is presented, which includes variable exponent Lebesgue spaces, the maximal operator, the generalized Muckenhoupt condition, and transfer techniques.

TL;DR: A thorough introduction to the variational analysis of nonlinear problems described by nonlocal operators can be found in this paper, where the authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of equations, plus their application to various processes arising in the applied sciences.

TL;DR: In this article, the existence of solutions for equations driven by a non-local integrodifferential operator with homogeneous Dirichlet boundary conditions was studied and a nonlinear solution for them using the Mountain Pass Theorem was found.

TL;DR: In this paper, sign changing solutions of nonlocal quasilinear elliptic boundary value problems using variational methods and invariant sets of descent flow were obtained for the first time.