We prove scattering below the mass–energy threshold for focusing inhomogeneous nonlinear Schrödinger equation iut+Δu+|x|−b|u|p−1u=0,when b≥0 and N>2 in intercritical case 0<sc<1. This work generalizes results of Farah Guzmán (2019), allowing a broader range values parameters p b. use modified version Dodson–Murphy’s approach (Dodson Murphy, 2017) us to deal with inhomogeneity. The proof is also...

We consider an equation with exponential nonlinearity under the Dirichlet boundary condition. For a one- or two-dimensional domain, global solution has been obtained. In this paper, to extend result higher dimensional case, we concentrate on radial solutions in annulus. First, construct time-local abstract theory of differential equations. Next, show that decreasing energy exists problem. Final...

The Schrödinger equation with the central potential is first studied in the arbitrary dimensional spaces and obtained an analogy of the two-dimensional Schrödinger equation for the radial wave function through a simple transformation. As an example, applying an ansatz to the eigenfunctions, we then arrive at an exact closed form solution to the modified two-dimensional Schrödinger equation with...

We obtain infinitely many non-radial singular solutions of LaneEmden equation ∆u + u = 0 in RN\{0}, N ≥ 4 with N + 1 N − 3 < p < pc(N − 1) by constructing infinitely many radially symmetric regular solutions of equation on SN−1 ∆SN−1w − 2 p− 1 [ N − 2− 2 p− 1 ] w + w = 0.