this study concerns the existence and multiplicity of positive weak solutions for a class ofsemilinear elliptic systems with nonlinear boundary conditions. our results is depending onthe local minimization method on the nehari manifold and some variational techniques. alsoby using mountain pass lemma, we establish the existence of at least one solution withpositive energy.

We study the elliptic system \begin{equation*} \begin{cases} -\Delta u_1 - \kappa_1u_1 = \mu_1|u_1|^{p-2}u_1 + \lambda\alpha|u_1|^{\alpha-2}|u_2|^\beta u_1, \\ u_2 \kappa_2u_2 \mu_2|u_2|^{p-2}u_2 \lambda\beta|u_1|^\alpha|u_2|^{\beta-2}u_2, u_1,u_2\in D^{1,2}_0(\Omega), \end{cases} \end{equation*} where $\Omega$ is a bounded domain in $\mathbb R^N$, $N\geq 3$, $\kappa_1,\kappa_2\in\mathbb R$, $\...

In this paper we explore different hardware accelerators for cryptography based on elliptic curves. Furthermore, we present a hierarchical multiprocessor system-onchip (MPSoC) platform that can be used for fast integration and evaluation of novel hardware accelerators. In respect of two application scenarios the hardware accelerators are coupled at different hierarchy levels of the MPSoC platfo...

Models for distributed capacitance in a thin lm are derived in the form of a system of local RC diiusion equations coupled by a global elliptic equation. Such models contain the local geometry of the distributed capacitance on which charge is stored and the exchange of current ux on its interface with the medium. Certain singular limits are characterized, and the resulting degenerate initial-bo...

We establish the existence of a solution to a non-linearly coupled elliptic-parabolic system of PDEs describing the single-phase, miscible displacement of one incompressible fluid by another in a porous medium. We consider a velocity-dependent diffusion-dispersion tensor and model the action of injection and production wells by measures on the domain. We obtain the solution by passing to the li...

The conformal formulation of the Einstein constraint equations is first reviewed, and we then consider the design, analysis, and implementation of adaptive multilevel finite element-type numerical methods for the resulting coupled nonlinear elliptic system. We derive weak formulations of the coupled constraints, and review some new developments in the solution theory for the constraints in the ...