Radial symmetry of ground states for a regional fractional Nonlinear Schrödinger Equation

Entire solutions for critical $p$-fractional Hardy Schrödinger Kirchhoff equations

“…While if K ∞ > 0, then there exists λ * = λ * (γ) > 0 such that for any λ ≥ λ * problem (1.1) admits a nontrivial radial mountain pass solution u γ,λ , which satisfies again (1.6). Theorem 1.2 extends in several directions the existence results obtained in [17,26,27,44] and the references cited therein.…”

The overdetermined equations on bounded domain

“…Due to the equivalence, the results are also established for the solutions of the problem (1.10). In order to learn more about the properties for the solutions of other kinds of equations, we can refer to [28][29][30][31] and the references therein.…”

Multiplicity and symmetry results for a nonlinear Schrödinger equation with non‐local regional diffusion

“…Very recently, Felmer and Torres considered positive solutions of nonlinear Schrödinger equation with non‐local regional diffusion The operator is a variational version of the non‐local regional Laplacian, defined by Under suitable assumptions on the nonlinearity f and the range of scope ρ , they obtained the existence of a ground state by mountain pass argument and a comparison method devised by Rabinowitz in for α = 1. Furthermore, they analysed symmetry properties and concentration phenomena of these solutions.…”

“…Motivated by these previous result, in this paper, we are interested in extending the recent result studied in [1,20] in the sense that we considered the multiplicity of solutions for the nonlinear Schrödinger equation (2) with x-dependence nonlinearity, and in a particular case, we obtain a symmetry result.…”

“…Very recently, Felmer and Torres [1,20] considered positive solutions of nonlinear Schrödinger equation with non-local regional diffusion…”