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Apr 09, 2025Open Access
This paper is devoted to the normalized solutions of a planer L2-critical Schrödinger-Poisson system with an external potential V(x) =❘X❘ 2 and in-homogeneous attractive interactions K(x)∈(0,1). Applying the constraint variational method, we prove that the normalized solutions exist if and only if the interaction strength a satisfies a∈(0,a *):=∥Q∥ 2L2...
Feb 18, 2025Open Access
Many kinds of explicit and exact solutions of the nonlinear Newell equation, including the solitary wave solution, the singular traveling wave solution, and the triangle function-type periodic wave solutions, are presented by a direct trial function approach.
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.
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