Note on the form of a first-order partial differential equation

A RESEARCH NOTE ON THE SECOND ORDER DIFFERENTIAL EQUATION

Let U(t, ) be solution of the Dirichlet problem y''+( t-q(t))y= 0 - 1 t l y(-l)= 0 = y(x), with variabIe t on (-1, x), for fixed x, which satisfies the initial condition U(-1, )=0 , (-1, )=1. In this paper, the asymptotic representation of the corresponding eigenfunctions of the eigen values has been investigated . Furthermore, the leading term of the asymptotic formula for ...

A method for solving first order fuzzy differential equation

Optimization of First Order Partial Differential Inclusions in Gradient Form

This paper is dedicated to optimization of socalled first order differential (PC) inclusions in gradient form on a square domain. As a supplementary problem, discreteapproximation problem is considered. In the Euler-Lagrange form, necessary and sufficient conditions are derived for partial differential inclusions (PC). The results obtained are based on a new concept of locally adjoint mappings.

on the cases of explicit solvability of a third order partial differential equation

in this paper, the goursat problem of a third order equation on cases of explicit solvability isinvestigated, with the help of the riemann function. some results and one theorem are given concerning theexistence and uniqueness for the solution of the suggested problem.

First Order Partial Differential Equations

If T⃗ denotes a vector tangent to C at t,x,u then the direction numbers of T⃗ must be a,b, f. But then (1.2) implies that T⃗ n⃗, which is to say, T⃗ lies in the tangent plane to the surface S. But if T⃗ lies in the tangent plane, then C must lie in S. Evidently, solution curves of (1.2) lie in the solution surface S associated with (1.2). Such curves are called characteristic curves for (1.2). W...