Related papers: Note on a Nonlinear Differential Equation
It is well recognized that new types of exact travelling wave solutions to nonlinear partial differential equations can be obtained by modifications of the methods which are in hand. In this study, we extend the class of auxiliary equations…
A general formalism to solve nonlinear differential equations is given. Solutions are found and reduced to those of second order nonlinear differential equations in one variable. The approach is uniformized in the geometry and solves…
New problem is considered that is to find nonlinear differential equations with special solutions. Method is presented to construct nonlinear ordinary differential equations with exact solution. Crucial step to the method is the assumption…
In this paper we show how to find a closed form solution for third order difference operators in terms of solutions of second order operators. This work is an extension of previous results on finding closed form solutions of recurrence…
Based on the analysis of a certain class of linear operators on a Banach space, we provide a closed form expression for the solutions of certain linear partial differential equations with non-autonomous input, time delays and stochastic…
Simple form scalar differential equation with delay and non-linear negative periodic feedback is considered. The existence of slowly oscillating periodic solutions with the same period as the feedback coefficient is shown numerically within…
The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied. However, nonlinear partial differential equations (PDEs) pose substantial challenges from an…
In this paper, we prove the partial linearization for n-dimensional nonautonomous differential equations. The conditions are formulated in terms of the dichotomy spectrum.
In this paper we show some explicit results regarding non-linear diffusive equations on Poincar\'e half plane. We obtain exact solutions by using the generalized separation of variables and we also show the meaning of these results in the…
In this paper are examined general classes of linear and non-linear analytical systems of partial differential equations. Indeed the integrability conditions are found and if they are satisfied, the solutions are given as functional series…
A functional differential equation related to the logistic equation is studied by a combination of numerical and perturbation methods. Parameter regions are identified where the solution to the nonlinear problem is approximated well by…
A nonlinear inequality is formulated in the paper. An estimate of the rate of decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can be…
In order to find closed form solutions of nonintegrable nonlinear ordinary differential equations, numerous tricks have been proposed. The goal of this short review is to recall classical, 19th-century results, completed in 2006 by…
We establish the existence of weak solutions of a nonlinear radiation-type boundary value problem for elliptic equation on divergence form with discontinuous leading coefficient. Quantitative estimates play a crucial role on the real…
We analyze solvability of a special form of distributed order fractional differential equations within the space of tempered distributions supported by the positive half-line.
Differential equations with constant and variable coefficients over octonions are investigated. It is found that different types of differential equations over octonions can be resolved. For this purpose non-commutative line integration is…
The determinant of a lower Hessenberg matrix (Hessenbergian) is expressed as a sum of signed elementary products indexed by initial segments of nonnegative integers. A closed form alternative to the recurrence expression of Hessenbergians…
The paper develops the method for construction of families of particular solutions to some classes of nonlinear Partial Differential Equations (PDE). Method is based on the specific link between algebraic matrix equations and PDE.…
In this paper, we introduce some new ideas to study Schrodinger equations in RN with power-type nonlinearities.
A theorem providing necessary conditions enabling one to map a nonlinear system of first order partial differential equations to an equivalent first order autonomous and homogeneous quasilinear system is given. The reduction to quasilinear…