Displaying similar documents to “On existence theorems for semilinear equations and applications”

On the solvability of the Lyapunov equation for nonselfadjoint differential operators of order 2m with nonlocal boundary conditions

Aris Tersenov (2001)

Annales Polonici Mathematici

Similarity:

This paper is devoted to the solvability of the Lyapunov equation A*U + UA = I, where A is a given nonselfadjoint differential operator of order 2m with nonlocal boundary conditions, A* is its adjoint, I is the identity operator and U is the selfadjoint operator to be found. We assume that the spectra of A* and -A are disjoint. Under this restriction we prove the existence and uniqueness of the solution of the Lyapunov equation in the class of bounded operators.

Positive solutions with given slope of a nonlocal second order boundary value problem with sign changing nonlinearities

P. Ch. Tsamatos (2004)

Annales Polonici Mathematici

Similarity:

We study a nonlocal boundary value problem for the equation x''(t) + f(t,x(t),x'(t)) = 0, t ∈ [0,1]. By applying fixed point theorems on appropriate cones, we prove that this boundary value problem admits positive solutions with slope in a given annulus. It is remarkable that we do not assume f≥0. Here the sign of the function f may change.

A topological version of the Ambrosetti-Prodi theorem

Bogdan Przeradzki (1996)

Annales Polonici Mathematici

Similarity:

The existence of at least two solutions for nonlinear equations close to semilinear equations at resonance is obtained by the degree theory methods. The same equations have no solutions if one slightly changes the right-hand side. The abstract result is applied to boundary value problems with specific nonlinearities.

A characterization of evolution operators

Naoki Tanaka (2001)

Studia Mathematica

Similarity:

A class of evolution operators is introduced according to the device of Kato. An evolution operator introduced here provides a classical solution of the linear equation u'(t) = A(t)u(t) for t ∈ [0,T], in a general Banach space. The paper presents a necessary and sufficient condition for the existence and uniqueness of such an evolution operator.