相关论文: Homoclinic Solution to Zero of a Non-autonomous, N…
We deal with the non-autonomous parameter-dependent second-order differential equation \begin{equation*} \delta \left( \dfrac{v'}{\sqrt{1-(v')^{2}}} \right)' + q(t) f(v)= 0, \quad t\in\mathbb{R}, \end{equation*} driven by a…
We study the existence of homoclinic type solutions for second order Lagrangian systems of the type $\ddot{q}(t)-q(t)+a(t)\nabla G(q(t))=f(t)$, where $t\in\mathbb{R}$, $q\in\mathbb{R}^n$, $a\colon\mathbb{R}\to\mathbb{R}$ is a continuous…
In this paper we present sufficient conditions for the existence of heteroclinic or homoclinic solutions for second order coupled systems of differential equations on the real line. We point out that it is required only conditions on the…
In this paper, we use variational methods to prove the existence of heteroclinic solutions for a class of non-autonomous second-order equation.
We establish the existence of homoclinic solutions for suitable systems of nonlocal equations whose forcing term is of gradient type. The elliptic operator under consideration is the fractional Laplacian and the potentials that we take into…
In this paper, we mainly consider the existence of infinitely many homoclinic solutions for a class of subquadratic second-order Hamiltonian systems $\ddot{u}-L(t)u+W_u(t,u)=0$, where $L(t)$ is not necessarily positive definite and the…
We develop a stable and high-order accurate discontinuous Galerkin method for the second order wave equation, specifically designed to handle nonsmooth solutions. Our approach integrates the energy-based discontinuous Galerkin method with…
We propose a numerical method to approximate the solution of second order elliptic problems in nonvariational form. The method is of Galerkin type using conforming finite elements and applied directly to the nonvariational (nondivergence)…
We show that a class of divergence-form elliptic problems with quadratic growth in the gradient and non-coercive zero order terms are solvable, under essentially optimal hypotheses on the coefficients in the equation. In addition, we prove…
We consider a class of time dependent second order partial differential equations governed by a decaying entropy. The solution usually corresponds to a density distribution, hence positivity (non-negativity) is expected. This class of…
We show the existence of homoclinic type solutions of second order Hamiltonian systems with a potential satisfying a relaxed superquadratic growth condition and a forcing term that is sufficiently small in the space of square integrable…
In this article, we study about the solutions of second order linear differential equations by considering several conditions on the coefficients of homogenous linear differential equation and its associated non-homogenous linear…
In the paper, we utilize the recent variational, abstract theorem to show the existence of homoclinic solutions to the Hamiltonian system $$ \dot{z} = J D_z H(z, t), \quad t \in \mathbb{R}, $$ where the Hamiltonian $H : \mathbb{R}^{2N}…
This study discusses a class of linear systems of fractional differential equations with non-constant coefficients, with a particular focus on problems exhibiting highly oscillatory and non-smooth behavior. We first establish the regularity…
In this paper, we study the existence and multiplicity of homoclinic solutions for following Hamiltonian systems with asymptotically quadratic nonlinearities at infinity \begin{eqnarray*} \ddot{u}(t)-L(t)u+\nabla W(t,u)=0. {eqnarray*} We…
In this paper we consider the first order discrete Hamiltonian system $$\begin{cases} x_1(n+1)-x_1(n)& =- H_{x_2}(n,x(n)), x_2(n)-x_2(n-1)& =\ \ H_{x_1}(n,x(n)). \end{cases} $$ Where $n\in \mathbb{Z}$, $x(n)=$ $x_1 (n) \choose x_2 (n)$$ \in…
We study both existence and nonexistence of nonnegative solutions for nonlinear elliptic problems with singular lower order terms that have natural growth with respect to the gradient, whose model is $$ \begin{cases} -\Delta u +…
This article deals with the second order linear differential equations with entire coefficients. We prove some results involving conditions on coefficients so that the order of growth of every non-trivial solution is infinite.
In this paper, we study the existence, regularity, and approximation of the solution for a class of nonlinear fractional differential equations. {In order to do this}, suitable variational formulations are defined for a nonlinear boundary…
In this paper we discuss the local discontinuous Galerkin methods coupled with two specific explicit-implicit-null time discretizations for solving one-dimensional nonlinear diffusion problems $U_t=(a(U)U_x)_x$. The basic idea is to add and…