Existence of a positive solution for a class of fractional elliptic problems in exterior domains involving critical growth

Multiple Normalized Solutions to a Choquard Equation Involving Fractional p-Laplacian in ℝN

“…For the supercritical growth case, Li and Wang [8] obtained the existence of a nontrivial solution to p-Laplacian equations in R N using the Moser iteration and perturbation arguments. For more interesting results, see [9][10][11][12] and their references.…”

“…is the critical Sobolev exponent. They proved that problem (10) has a normalized solution with constrained variational methods. Zhang and Zhang [24] is the first paper to study the following p-Laplacian equation:…”

Probabilistic representations of solutions of nonlinear PDEs

“…On the other hand, a large part of the litterature on fractional PDEs with nonlinearities is devoted to proving the nonexistence of trivial solutions when the initial datum φ vanishes outside Bp0, Rq and c 0 pxq " 0 in (3.1), see, e.g., [4], [76], [27]. This also includes the method of moving spheres, see [28], [31], and the use of the Pohoazev identity for the fractional Laplacian, see [67,69].…”