Boundary value problems for linear partial differential equation with constant coefficients. Homogeneous equation in the half plane

An analytic solution for a non-local initial-boundary value problem including a partial differential equation with variable coefficients

‎This paper considers a non-local initial-boundary value problem containing a first order partial differential equation with variable coefficients‎. ‎At first‎, ‎the non-self-adjoint spectral problem is derived‎. ‎Then its adjoint problem is calculated‎. ‎After that‎, ‎for the adjoint problem the associated eigenvalues and the subsequent eigenfunctions are determined‎. ‎Finally the convergence ...

an analytic solution for a non-local initial-boundary value problem including a partial differential equation with variable coefficients

‎this paper considers a non-local initial-boundary value problem containing a first order partial differential equation with variable coefficients‎. ‎at first‎, ‎the non-self-adjoint spectral problem is derived‎. ‎then its adjoint problem is calculated‎. ‎after that‎, ‎for the adjoint problem the associated eigenvalues and the subsequent eigenfunctions are determined‎. ‎finally the convergence ...

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation

on the goursat problem for a linear partial differential equation

in this paper, the goursat problem of a general form for a linear partial differential equation is investigated with the help of the riemann function method. some results are given concerning the existence and uniqueness for the solution of the suggested problem.

Nontrivial Solutions for Boundary Value Problems of Nonlinear Differential Equation

The nonlinear three-point boundary value problem { −u′′(t) = f(t, u(t)), t ∈ I, βu(0)− γu′(0) = 0, u(1) = αu(η), is discussed under some conditions concerning the first eigenvalue corresponding to a special linear operator, where I = [0, 1], η ∈ (0, 1), α, β, γ ∈ [0,∞) with β + γ 6= 0, f : [0, 1] × (−∞,+∞) → (−∞,+∞) is sign–changing continuous function and may be unbounded from below. By applyi...