Given a conformally transversally anisotropic manifold (M, g), we consider the semilinear elliptic equation $$\begin{aligned} (-\Delta _{g}+V)u+qu^2=0\quad \hbox { on}\ M. \end{aligned}$$ We show that an priori unknown smooth function q can be uniquely determined from knowledge of Dirichlet-to-Neumann map associated to equation. This extends previously known results works Feizmohammadi and Oksa...

Abstract A one–spatial dimensional tumour growth model Breward et al. ( 2001, 2002, 2003) that consists of three dependent variables space and time is considered. These are volume fraction cells, velocity nutrient concentration. The satisfy a coupled system semilinear advection equation (hyperbolic), simplified linear Stokes (elliptic), diffusion (parabolic) with appropriate conditions on the t...

3 Semilinear equations with absorption 19 3.1 The Marcinkiewicz spaces approach . . . . . . . . . . . . . . . . . . . . . . 21 3.2 Admissible measures and the ∆2-condition . . . . . . . . . . . . . . . . . . . 26 3.3 The duality method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.3.1 Bessel capacities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.3.2 Sharp...

We consider a class of semilinear elliptic problems in twoand three-dimensional domains with conical points. We introduce Sobolev spaces with detached asymptotics generated by the asymptotical behaviour of solutions of corresponding linearized problems near conical boundary points. We show that the corresponding nonlinear operator acting between these spaces is Fréchet differentiable. Applying ...

We study the well posedness of nonlinear Schrödinger (NLS) equation with a point interaction and power nonlinearity in dimension two three. Behind autonomous interest problem, this is model evolution so called singular solutions that are known analysis semilinear elliptic equations. show Cauchy problem for NLS considered enjoys local existence uniqueness strong (operator domain) solutions, depe...