LRES, Faculty of Sciences Tunis, University Tunis El Manar, Tunisia EM [email protected] KW Asymptotically linear % variational method Schr?dinger equations Cerami sequence KR nema In this paper, we investigate a quasilinear problem under Dirichlet boundary condition in regular domain with asymptotically nonlinearities. We use version the mountain pass theorem to prove existence solution ...

in this paper, first a new homotopy perturbation method for solving a fractional order nonlinear telegraph equation is introduced. by applying the proposed method, the nonlinear equation is translated to linear equations for per iteration of homotopy perturbation method. then, the obtained problems are solved with separation method. in the examples, it is illustrated that the exact solution is ...

in this paper, we propose a new method for solving the stochastic advection-diffusion equation of ito type. in this work, we use a compact finite difference approximation for discretizing spatial derivatives of the mentioned equation and semi-implicit milstein scheme for the resulting linear stochastic system of differential equation. the main purpose of this paper is the stability investigatio...

In 1934, H. Whitney asked how one can determine whether a real-valued function on a closed subset of Rn is the restriction of a Cm-function on Rn. A complete answer to this question was found much later by C. Fefferman in the early 2000s. Here, we work in an o-minimal expansion of a real closed field and solve the C1-case of Whitney’s Extension Problem in this context. Our main tool is a defina...

A linear equation is r-regular, if, for every r-coloring of the positive integers, there exist positive integers of the same color which satisfy the equation. In 2005, Fox and Radoićič conjectured that the equation x1 +2x2 + · · ·+2xn−1−2xn = 0, for any n > 2, has a degree of regularity of n−1, which would verify a conjecture of Rado from 1933. Rado’s conjecture has since been verified with a d...

High energy scattering is considered within the framework of the QCD dipole model formulated as a classical branching process. Starting from Mueller’s generating functional we derive the high energy evolution law for the scattering amplitude. The amplitude’s evolution is given by an infinite hierarchy of linear equations equivalent to Balitsky’s chain reduced to dipole operators. We comment abo...

In this paper we study the oscillation of solutions to the half-linear differential equation (r(t)|y′|p−1 sgn y)′ + c(t)|y|p−1 sgn y = 0, under the assumptions R∞ r1/(1−p)(s) ds < ∞, r(t) > 0, p > 1. Our main tool is a Riccati type transformation for using the so called “function sequence technique”. This method leads to new and to known oscillation and comparison results. We also give an examp...