ﻻ يوجد ملخص باللغة العربية
This paper is devoted to a comprehensive study of the nonlinear Schrodinger equations with combined nonlinearities of the power-type and Hartree-type in any dimension nge3. With some structural conditions, a nearly whole picture of the interactions of these nonlinearities in the energy space is given. The method is based on the Morawetz estimates and perturbation principles.
We investigate normalized solutions for the Schr{o}dinger equation with combined Hartree type and power nonlinearities, namely begin{equation*} left{ begin{array}{ll} -Delta u+lambda u=gamma (I_{alpha }ast leftvert urightvert ^{p})|u|^{p-2}u+mu |u|^{
We study inverse problems for semilinear elliptic equations with fractional power type nonlinearities. Our arguments are based on the higher order linearization method, which helps us to solve inverse problems for certain nonlinear equations in cases
In this paper, we study the existence and asymptotic properties of solutions to the following fractional Kirchhoff equation begin{equation*} left(a+bint_{mathbb{R}^{3}}|(-Delta)^{frac{s}{2}}u|^{2}dxright)(-Delta)^{s}u=lambda u+mu|u|^{q-2}u+|u|^{p-2}u
In this note we consider differential equations driven by a signal $x$ which is $gamma$-Holder with $gamma>1/3$, and is assumed to possess a lift as a rough path. Our main point is to obtain existence of solutions when the coefficients of the equatio
In this paper, we consider the following nonlinear Schr{o}dinger equations with mixed nonlinearities: begin{eqnarray*} left{aligned &-Delta u=lambda u+mu |u|^{q-2}u+|u|^{2^*-2}uquadtext{in }mathbb{R}^N, &uin H^1(bbr^N),quadint_{bbr^N}u^2=a^2, endalig