In the first part of this chapter we focus on the question of well-posedness of boundary-value problems for linear partial differential equations of elliptic type. The second part is devoted to the construction and the error analysis of finite difference schemes for these problems. It will be assumed throughout that the coefficients in the equation, the boundary data and the resulting solution ...

This paper is concerned with the existence of extreme solutions of integral boundary value problems for a class of first order impulsive functional differential equations. We obtain the sufficient conditions for existence of extreme solutions by using upper and lower solutions method coupled with monotone iterative technique. An example is also discussed to illustrate the efficiency of the obta...

This paper is concerned with the anti-periodic boundary value problems for nonlinear impulsive functional differential equations  x′(t) = f(t, x(t), x(α1(t)), · · · , x(αn(t))), a.e. t ∈ [0, T ], ∆x(tk) = Ik(x(tk)), k = 1, · · · ,m, x(0) = −x(T ). The sufficient conditions for the existence of at least one solution to above problem are established. The results generalize and improve the kno...

We develop a general theorem concerning the existence of solutions to the periodic boundary value problem for the first-order impulsive differential equation,    x′(t) = f(t, x(t)), t ∈ J \ {t1, t2, · · · , tk} 4x(ti) = Ii(x(ti)), i = 1, 2 · · · k x(0) = x(T ). And using it we get a concrete existence result. Moreover, to our knowledge the coincidence degree method has not been used to t...