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Existence of solution to nonlinear boundary value problem for ordinary differential equation of the second order in Hilbert space

Eva Rovderová (1992)

Mathematica Bohemica

In this paper we deal with the boundary value problem in the Hilbert space. Existence of a solutions is proved by using the method of lower and upper solutions. It is not necessary to suppose that the homogeneous problem has only the trivial solution. We use some results from functional analysis, especially the fixed-point theorem in the Banach space with a cone (Theorem 4.1, [5]).

Existence of solutions for hyperbolic differential inclusions in Banach spaces

Nikolaos S. Papageorgiou (1992)

Archivum Mathematicum

In this paper we examine nonlinear hyperbolic inclusions in Banach spaces. With the aid of a compactness condition involving the ball measure of noncompactness we prove two existence theorems. The first for problems with convex valued orientor fields and the second for problems with nonconvex valued ones.

Existence of solutions for integrodifferential inclusions in Banach spaces

Nikolaos S. Papageorgiou (1991)

Commentationes Mathematicae Universitatis Carolinae

In this paper we examine nonlinear integrodifferential inclusions defined in a separable Banach space. Using a compactness type hypothesis involving the ball measure of noncompactness, we establish two existence results. One involving convex-valued orientor fields and the other nonconvex valued ones.

Existence of solutions of perturbed O.D.E.'s in Banach spaces

Giovanni Emmanuele (1991)

Commentationes Mathematicae Universitatis Carolinae

We consider a perturbed Cauchy problem like the following (PCP) x ' = A ( t , x ) + B ( t , x ) x ( 0 ) = x 0 and we present two results showing that (PCP) has a solution. In some cases, our theorems are more general than the previous ones obtained by other authors (see [4], [8], [9], [11], [13], [17], [18]).

Existence of solutions of the dynamic Cauchy problem on infinite time scale intervals

Ireneusz Kubiaczyk, Aneta Sikorska-Nowak (2009)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In the paper, we prove the existence of solutions and Carathéodory’s type solutions of the dynamic Cauchy problem x Δ ( t ) = f ( t , x ( t ) ) , t ∈ T, x(0) = x₀, where T denotes an unbounded time scale (a nonempty closed subset of R and such that there exists a sequence (xₙ) in T and xₙ → ∞) and f is continuous or satisfies Carathéodory’s conditions and some conditions expressed in terms of measures of noncompactness. The Sadovskii fixed point theorem and Ambrosetti’s lemma are used to prove the main result. The results presented...

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