Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userInverse problems for elliptic equations with fractional power type nonlinearities
248
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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 where the solution for a corresponding linear equation is not known. By using a fractional order adaptation of this method, we show that the results of [LLLS20a, LLLS20b] remain valid for general power type nonlinearities.
rate research
Read More
In this paper, we prove the existence of nontrivial unbounded domains $Omegasubsetmathbb{R}^{n+1},ngeq1$, bifurcating from the straight cylinder $Btimesmathbb{R}$ (where $B$ is the unit ball of $mathbb{R}^n$), such that the overdetermined elliptic problem begin{equation*} begin{cases} Delta u +f(u)=0 &mbox{in $Omega$, } u=0 &mbox{on $partialOmega$, } partial_{ u} u=mbox{constant} &mbox{on $partialOmega$, } end{cases} end{equation*} has a positive bounded solution. We will prove such result for a very general class of functions $f: [0, +infty) to mathbb{R}$. Roughly speaking, we only ask that the Dirichlet problem in $B$ admits a nondegenerate solution. The proof uses a local bifurcation argument.
We consider inverse boundary value problems for general real principal type differential operators. The first results state that the Cauchy data set uniquely determines the scattering relation of the operator and bicharacteristic ray transforms of lower order coefficients. We also give two different boundary determination methods for general operators, and prove global uniqueness results for determining coefficients in nonlinear real principal type equations. The article presents a unified approach for treating inverse boundary problems for transport and wave equations, and highlights the role of propagation of singularities in the solution of related inverse problems.
We investigate partial symmetry of solutions to semi-linear and quasi-linear elliptic problems with convex nonlinearities, in domains that are either axially symmetric or radially symmetric.
In this article, we establish the existence of solutions to the fractional $p-$Kirchhoff type equations with a generalized Choquard nonlinearities without assuming the Ambrosetti-Rabinowitz condition.
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.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
