The Schr枚dinger equation (1) $Delta u + f(x,u) = 0$ is considered in an exterior domain $Omega $ in $R^n ,n geqq 2$, where f is H枚lder continuous and nonnegative and ${f(x,u)} / {u}$ is majorized above and below by nonnegative functions $g(| x |,u)$ which ...
Radial-spherical decompositionWe solve semilinear Schrdinger equations with a singular potential of inverse-square scale, especially the threshold of nonnegativity and selfadjointness.doi:10.1016/j.jde.2019.11.087Toshiyuki SuzukiJournal of Differential Equations...
Bounded Positive Solutions of Semilinear Schrödinger Equations The Schr枚dinger equation (1) $\\Delta u + f(x,u) = 0$ is considered in an exterior domain $\\Omega $ in $R^n ,n \\geqq 2$, where f is H枚lder continuous and nonnegative and ${f(x,u)} / {u}$ is majorized...
The methods involve, first, reduction of the Schrdinger equations to group-invariant semilinear complex 2nd order ordinary differential equations (ODEs) with respect to an optimal set of one-dimensional point symmetry groups, and second, use of inherited symmetries, hidden symmetries, and conditional ...
Soliton solutions for quasilinear Schrdinger equations with critical growth Soliton solutions for quasilinear Schrödinger equations with critical growthSoliton solutions for quasilinear Schrödinger equations with critical growthSchrödin... Jo?o M. Bezerra do ó,OH Miyagaki,SHM Soares - 《Journal...
We prove the existence of a positive solution of the Dirichlet problem for the Schrdinger equation whose potential possesses a critical singularity. It is assumed that the boundary of the domain is average concave in a neighborhood of the origin. Bibliography: 13 titles....
Tang X H. Infinitely many solutions for semilinear Schr?dinger equations with sign-changing potential and nonlinearity[J]. Journal of Mathematical Analysis and Applications, 2013, 401(1): 407-415.Multiplicity of solutions for a class of semilinear Schr?dinger equations with sign-changing potential[...
Soliton solutions for quasilinear Schrdinger equations: The critical exponential case Quasilinear elliptic equations in R 2 of second order with critical exponential growth are considered. By using a change of variable, the quasilinear equat... Jo?o M.B. do ó,OH Miyagaki,SHM Soares - 《...
Global Existence for Semilinear wave Equations in Exterior Domain; 外区域上半线性波动方程解的整体存在性 3. Existence and Uniqueness of Solution of a Class of Coupled Semilinear Schr dinger Equations; 一类半线性耦合Schr dinger方程组解的存在唯一性 ...
Quasi-periodic solutions for fully nonlinear forced reversible Schrdinger equations Note that this is the first result on analytic quasi-periodic solutions for fully nonlinear PDEs.In the forced cases we use a Nash-Moser scheme on scales of Sobolev spaces combined with a re- ducibility argument ...