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Dec 27, 2023Open Access
In this paper, we consider the following nonlinear Choquard equation -ε 2Δw V(x)w=ε -θ(Y1(w) Y2(w)), where ε>0, N>2, Y1(w):= W1(x)[I θ*( W1|w| p)]|w| p-2w, Y2(w):= W2(x)[I θ*( W2|w| q)]|w| q-2w, I θ is the Riesz pote...
Nov 23, 2023Open Access
In this paper, we study a nonlinear Schrödinger equation with competing potentials -ε 2Δν V(x)ν=W 1(x)|ν| p-2ν W 2(x)|ν| q-2ν, ν∈H 1(R N), where ε>0, p,q∈(2,2*), p>q, , V(x), W 1(x) and W 2(x) are continuous bounded positive functions. Under suitable assumptions on the potentials, we consider the existence, concentration, convergence and decay estima...
Jun 14, 2023Open Access
In this study, we have determined Green’s functions for Helmholtz integral equations in a spherical polar coordinate system in the whole plane domain with the aid of spectral Fourier transform technique. Our intended Green’s function solution has a dominant role to represent wave propagation with a high quantum wave number. The Diracdelta function also plays an important role here to represent the scattering region for wave propagation. The evaluation of the improper double integrals in the comp...
Sep 16, 2022Open Access
In this paper, we study the fractional Klein-Gordon-Maxwell system with steep potential well. On the basis of overcoming the lack of compactness, the ground state solution is obtained by proving that the solution satisfies the mountain pass level.
Aug 18, 2022Open Access
In this paper, we study the nonautonomous Klein-Gordon-Maxwell system with logarithmic nonlinearity. We obtain the existence of nontrivial solution for this system by logarithmic Sobolev inequality and variational method.
Feb 28, 2022Open Access
In this paper, we prove the existence of global strong solutions for the three-dimensional nonautonomous Brinkman-Forchheimer-extended-Darcy equation with singularly oscillating and show that the strong solutions are unique. In addition, we also give general estimates for its auxiliary linear equation; finally, we derive the oscillatory averaged estimates of the equation from the results of these general estimates.
Feb 24, 2021Open Access
In this paper, we investigate the question of existence of nonnegative solution for some fractional boundary value problem involving p-Laplacian operator, The results presented in this thesis are based on fixed point theorem, more precisely, Krasnosilski fixed point theorem, on the cones to prove the existence of a fixed point for a mathematics operator and that fixed point is a solution to the given fractional equation by combining some properties of the associated Green function. We will study...
Oct 30, 2020Open Access
In this paper, we discuss the assumptions, the balances, and the constitutive relationships in order to provide a set of tools for the mathematical modeling of a geothermal system. In particular, we present a model for pressure and saturation supposing that: 1) the geothermal fluid flows in a porous medium, 2) it is composed of pure water, 3) the simultaneous presence of the gaseous (vapor) and liquid phases occurs, and 4) the effects of capillarity action can be introduced.
Apr 29, 2020Open Access
In this paper, a new iterative formula for solving ordinary and partial nonlinear differential equations is derived based on the combination between Bernstein’s polynomial and the Adomian decomposition formula. The solution of the differential equations has been transformed into iterative formulas that find the solution directly without the need to convert it into a non-linear system of equations and solving it by other numerical methods that require considerable time and effort. The obtained re...
Nov 28, 2019Open Access
In this paper, we study the existence and uniqueness of strong solution of a regularized model of the motion of a 3D nonlinear-viscous fluid with delay in the locally Lipschitz case, and further study the asymptotic behavior of solution.
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