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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.
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 pr
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 lo
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 o