On a semilinear elliptic equation with inverse-square potential

The nonlinear Schrödinger equation with an inverse-square potential

We discuss recent results on the scattering/blow-up dichotomy below the ground state threshold for the focusing nonlinear Schrödinger equation with an inverse-square potential and a nonlinearity that is mass-supercritical and energy-subcritical.

Uniqueness of Semilinear Elliptic Inverse Problem

We consider the uniqueness of the inverse problem for a semilinear elliptic differential equation with Dirichlet condition. The necessary and sufficient condition of a unique solution is obtained. We improved the results obtained by Isakov and Sylvester (1994) for the same problem.

A two-phase free boundary problem for a semilinear elliptic equation

In this paper we study a two-phase free boundary problem for a semilinear elliptic equation on a bounded domain $Dsubset mathbb{R}^{n}$ with smooth boundary‎. ‎We give some results on the growth of solutions and characterize the free boundary points in terms of homogeneous harmonic polynomials using a fundamental result of Caffarelli and Friedman regarding the representation of functions whose ...

Infinitely Many Solutions for a Semilinear Elliptic Equation with Sign-Changing Potential

Solving the inverse problem of determining an unknown control parameter in a semilinear parabolic equation

The inverse problem of identifying an unknown source control param- eter in a semilinear parabolic equation under an integral overdetermina- tion condition is considered. The series pattern solution of the proposed problem is obtained by using the weighted homotopy analysis method (WHAM). A description of the method for solving the problem and nding the unknown parameter is derived. Finally, tw...