Determining an unbounded potential for an elliptic equation with a power type nonlinearity
نویسندگان
چکیده
In this article we focus on inverse problems for a semilinear elliptic equation. We show that potential q in Ln/2+ε, ε>0, can be determined from the full and partial Dirichlet-to-Neumann map. This extends results [LLLS21b] where is shown Hölder continuous potentials. Also when map restricted to one point boundary, it possible determine Ln+ε. The authors of [ST22] proved true
منابع مشابه
Rupture Solutions of an Elliptic Equation with a Singular Nonlinearity
We construct infinitely many non-radial rupture solutions of the equation ∆u = 1 up in RN\{0}, u(0) = 0, N ≥ 3 with p > pc(N − 1) := N − 1− 2 √ N − 2 2 √ N − 2− (N − 5) .
متن کاملAn Elliptic Equation with No Monotonicity Condition on the Nonlinearity
An elliptic PDE is studied which is a perturbation of an autonomous equation. The existence of a nontrivial solution is proven via variational methods. The domain of the equation is unbounded, which imposes a lack of compactness on the variational problem. In addition, a popular monotonicity condition on the nonlinearity is not assumed. In an earlier paper with this assumption, a solution was o...
متن کاملan appropriate model for exchange rate predictability in iran: comparing potential forecastability
nowadays in trade and economic issues, prediction is proposed as the most important branch of science. existence of effective variables, caused various sectors of the economic and business executives to prefer having mechanisms which can be used in their decisions. in recent years, several advances have led to various challenges in the science of forecasting. economical managers in various fi...
Determining an Unbounded Potential from Cauchy Data in Admissible Geometries
In [4] anisotropic inverse problems were considered in certain admissible geometries, that is, on compact Riemannian manifolds with boundary which are conformally embedded in a product of the Euclidean line and a simple manifold. In particular, it was proved that a bounded smooth potential in a Schrödinger equation was uniquely determined by the Dirichlet-to-Neumann map in dimensions n ≥ 3. In ...
متن کاملA Fourth Order Nonlinear Elliptic Equation with Jumping Nonlinearity
We investigate the existence of solutions of the fourth order nonlinear elliptic boundary value problem under Dirichlet boundary condition A2u + CAU = bu+ + f in 0, where R is a bounded open set in Rn with smooth boundary and the nonlinearity bu+ crosses eigenvalues of A2 + CA. We also investigate a relation between multiplicity of solutions and source terms of the equation with the nonlinearit...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2023
ISSN: ['0022-247X', '1096-0813']
DOI: https://doi.org/10.1016/j.jmaa.2022.126962