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.

1 I n t r o d u c t i o n Elliptic curves can be applied to public-key cryptosystems, and as such several schemes have been proposed [3, 4, 5, 6, 9, 11]. There are two typical elliptic curve cryptosystems: E1Gamal-type scheme [4, 11] and RSA-type schemes [3, 5, 6]. The security of the EIGamal-type elliptic curve cryptosystem is based on the difficulty of solving a discrete logarithm over ellipt...

We employing a minimization arguments on appropriate Nehari manifolds, we obtain ground state solutionsfor non-local elliptic system driven by the fractional a(.)-Laplacian operator, with Dirichlet boundaryconditions type.

This paper surveys RSA-type implementations based on Lucas sequences and on elliptic curves. The main focus is the way how some known attacks on RSA were extended to LUC, KMOV and Demytko’s system. It also gives some directions for the choice of the most appropriate RSA-type system for a given application.

In this paper, we consider the existence of a non-trivial weaksolution to a quasilinear elliptic system involving critical Hardyexponents. The main issue of the paper is to understand thebehavior of these Palais-Smale sequences. Indeed, the principaldifficulty here is that there is an asymptotic competition betweenthe energy functional carried by the critical nonlinearities. Thenby the variatio...

The Riemann problem is solved for a system arising in chemotaxis. of mixed-type and transitions from hyperbolic to an elliptic region. It genuinely nonlinear the \begin{document}$ u $\end{document} - v plane except on -axis, where it linearly degenerate. We have physically relevant region up boundary hyperbolic-elliptic region, which non-strictly hyperbolic. also degenerate While solving proble...

In this paper we study local higher regularity properties of a linear elliptic system that is coupled with Maxwell-type. The result proved by means modified finite difference argument. These differences are based on inner variations combined Piola-type transformation in order to preserve the curl-structure Maxwell system. applied relaxed micromorphic model.

This paper is concerned with the system of Zakharov equations which involves the interactions between Langmuir and ion-acoustic waves in plasma. Abundant explicit and exact solutions of the system of Zakharov equations are derived uniformly by using the first integral method. These exact solutions are include that of the solitary wave solutions of bell-type for n and E, the solitary wave soluti...