Weakly nonlinear discrete multipoint boundary value problems

Boundary-Value Problems for Weakly Nonlinear Delay Differential Systems

and Applied Analysis 3 where the kernel K t, s is an n × n Cauchy matrix defined in the square a, b × a, b being, for every fixed s ≤ t , a solution of the matrix Cauchy problem LK ·, s t : ∂K t, s ∂t −A t Sh0K ·, s t Θ, K s, s I, 1.8 where K t, s ≡ Θ if a ≤ t < s ≤ b, Θ is n × n null matrix and I is n × n identity matrix. A fundamental n × n matrix X t for the homogeneous φ ≡ θ equation 1.5 ha...

Adjoints of Multipoint-integral Boundary Value Problems

The dual system to Ly=y'+Py, J_AtyOi)+ f1 K(t)v(t)dt = 0 is found when the setting is ¿°(0,1), 1 /2 -1 l/jj dt Kp' denote those vectors in X which are absolutely cont...

Discrete Boundary-value Problems

We consider multivariate sequences, deened by a partial linear recurrence equation together with appropriate boundary conditions. The domain of deenition of these sequences is the rst orthant of the integer lattice, restricted in some dimensions to an initial segment of the nonnegative integers. By means of the kernel method we obtain an explicit expression for the generating function of the so...

Nonlinear Discrete Periodic Boundary Value Problems at Resonance

Nonlinear Elliptic Boundary Value Problems

It is the object of the present note to present a new nonlinear version of the orthogonal projection method for proving the existence of solutions of nonlinear elliptic boundary value problems. The key point in this method is the application of a new general theorem concerning the solvability of nonlinear functional equations in a reflexive Banach space involving operators which may not be cont...