Adjoint operators and boundary value problems for linear differential equations
Admissible spaces for a first order differential equation with delayed argument
We consider the equation where and () are positive continuous functions for all and . By a solution of the equation we mean any function , continuously differentiable everywhere in , which satisfies the equation for all . We show that under certain additional conditions on the functions and , the above equation has a unique solution , satisfying the inequality where the constant does not depend on the choice of .
Adomian decomposition method for nonlinear Sturm-Liouville problems.
Affine-invariant monotone iteration methods with application to systems of nonlinear two-point boundary value problems
In this paper we present a new theorem for monotone including iteration methods. The conditions for the operators considered are affine-invariant and no topological properties neither of the linear spaces nor of the operators are used. Furthermore, no inverse-isotony is demanded. As examples we treat some systems of nonlinear ordinary differential equations with two-point boundary conditions.
Algebraic methods for solving boundary value problems.
By means of the reduction of boundary value problems to algebraic ones, conditions for the existence of solutions and explicit expressions of them are obtained. These boundary value problems are related to the second order operator differential equation X(2) + A1X(1) + A0X = 0, and X(1) = A + BX + XC. For the finite-dimensional case, computable expressions of the solutions are given.
Almost periodic Sturm-Liouville operators with Cantor homogeneous spectrum.
Ambarzumian's theorem for trees.
Ambrosetti-Prodi type results in a system of second and fourth-order ordinary differential equations.
An algebraic approach for solving boundary value matrix problems: existence, uniqueness and closed form solutions.
In this paper we show that in an analogous way to the scalar case, the general solution of a non homogeneous second order matrix differential equation may be expressed in terms of the exponential functions of certain matrices related to the corresponding characteristic algebraic matrix equation. We introduce the concept of co-solution of an algebraic equation of the type X^2 + A1.X + A0 = 0, that allows us to obtain a method of the variation of the parameters for the matrix case and further to find...
An Analysis and Improvement of the El~mistikawy and Werle Scheme
An application of a global bifurcation theorem to the existence of solutions for integral inclusions.
An application of the antimaximum principle for a fourth order periodic problem.
An application of the Leray-Schauder degree theory to boundary value problem for third and fourth order differential equations depending on the parameter
An approximation approach to eigenvalue intervals for singular boundary value problems with sign changing and superlinear nonlinearities.
An elliptic problem with arbitrarily small positive solutions.
An embedding theorem for a weighted space of Sobolev type and correct solvability of the Sturm-Liouville equation
An Equation With Left and Right Fractional Derivatives
An existence and multiplicity result for a periodic boundary value problem
A periodic boundary value problem for nonlinear differential equation of the second order is studied. Nagumo condition is not assumed on a part of nonlinearity. Existence and multiplicity results are proved using the method of lower and upper solutions. Results are applied to the generalized Liénard oscillator.
An existence principle for nonlocal difference boundary value problems with -Laplacian and its application to singular problems.
An existence result for a multipoint boundary value problem on a time scale.