Related papers: Nonlinear second order inhomogeneous differential …

A Lagrangian method is introduced recently for deriving indefinite integrals of special functions that satisfy homogeneous (nonhomogeneous) second-order linear differential equations. This paper extends this method to include indefinite…

During the past three decades, the advantageous concept of the Green's function has been extended from linear systems to nonlinear ones. At that, there exist a rigorous and an approximate extensions. The rigorous extension introduces the…

We consider the homogenization of a semilinear elliptic equation where the coefficients of the second-order differential operator may be discontinuous. We establish the existence and uniqueness of the fine-scale solution, followed by an a…

This paper deals with nonlinear singular partial differential equations of the form $t \partial u/\partial t=F(t,x,u,\partial u/\partial x)$ with independent variables $(t,x) \in \mathbb{R} \times \mathbb{C}$, where $F(t,x,u,v)$ is a…

The paper takles a procedure which allow to extend some linear, wave type equations to the study of nonlinear models. More concretely, we present a practical way to generate the largest class of a given form of second order differential…

This introduction to Green's functions is based on their role as kernels of differential equations. The procedures to construct solutions to a differential equation with an external source or with an inhomogeneity term are put together to…

In this paper, we analyze the solutions of the following non-linear differential-difference equations f^n(z) +\omega f^(n-1)f'(z) +p(z)f(z+c) = p_1e^{\alpha}_1z +p_2e^{\alpha}_2z and f^n(z)f'(z) +q(z)e^Q(z)f(z+c) = p_1e^{\alpha}_1z…

We consider second-order divergence form uniformly parabolic and elliptic PDEs with bounded and $VMO_{x}$ leading coefficients and possibly linearly growing lower-order coefficients. We look for solutions which are summable to the $p$th…

This article is devoted to deduce the expression of the Green's function related to a general constant coefficients fractional difference equation coupled to Dirichlet conditions. In this case, due to the points where some of the fractional…

The solvability in Sobolev spaces with special mixed norms is proved for nondivergence form second order parabolic equations. The leading coefficients are assumed to be measurable in the time variable and two coordinates of space variables,…

Motivated by the problem of solving the Einstein equations, we discuss high order finite difference discretizations of first order in time, second order in space hyperbolic systems.Particular attention is paid to the case when first order…

Partial differential equations are often used to model various physical phenomena, such as heat diffusion, wave propagation, fluid dynamics, elasticity, electrodynamics and image processing, and many analytic approaches or traditional…

This paper is devoted to study the nonlinear sequential fractional boundary value problems involving generalized $\psi$-Caputo fractional derivatives with nonlocal boundary conditions. We investigate the Green function and some of its…

Green's functions characterize the fundamental solutions of partial differential equations; they are essential for tasks ranging from shape analysis to physical simulation, yet they remain computationally prohibitive to evaluate on…

This work deals with the obtaining of solutions of first and second order Stieltjes differential equations. We define the notions of Stieltjes derivative on the whole domain of the functions involved, provide a notion of n-times…

In this paper, our focus lies on the study of the second-order variational analysis of orthogonally invariant matrix functions. It is well-known that an orthogonally invariant matrix function is an extended-real-value function defined on…

We present particular solutions for the following important nonlinear second order differential equations: modified Emden, generalized Lienard, convective Fisher, and generalized Burgers-Huxley. For the latter two equations these solutions…

We study the radial flow of retarded Green's function of energy-momentum tensor and $R$-current of dual gauge theory in presence of generic higher derivative terms in bulk Lagrangian. These are first order non-linear Riccati equations. We…

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.

This paper discusses properties of periodic functions, focusing on (systems of) partial differential equations with periodicity boundary conditions, called "cellular problems". These cellular problems arise naturally from the asymptotic…