### The interaction of linear boundary value and nonlinear functional conditions

The existence of solutions is studied for certain nonlinear differential equations with both linear and nonlinear conditions

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The existence of solutions is studied for certain nonlinear differential equations with both linear and nonlinear conditions

Asymptotically quadratic functions defined on Hilbert spaces are studied by using some results of the theory of Morse-Conley index. Applications are given to existence of nontrivial weak solutions for asymptotically linear elliptic partial and ordinary differential equations at resonances.

Existence results for critical points of asymptotically quadratic functions defined on Hilbert spaces are studied by using Morse-Conley index and pseudomonotone mappings. Applications to differential equations are given.

The Nielsen fixed point theory is used to show several results for certain operator equations involving weakly inward mappings.

We show that certain symmetries of maps imply the existence of their invariant curves.

The existence of classical solutions for some partial differential equations on tori is shown.

The paper deals with the bifurcation phenomena of heteroclinic orbits for diffeomorphisms. The existence of a Melnikov-like function for the two-dimensional case is shown. Simple possibilities of the set of heteroclinic points are described for higherdimensional cases.

For several specific mappings we show their chaotic behaviour by detecting the existence of their transversal homoclinic points. Our approach has an analytical feature based on the method of Lyapunov-Schmidt.

Ordinary differential inclusions depending on small parameters are considered such that the unperturbed inclusions are ordinary differential equations possessing manifolds of periodic solutions. Sufficient conditions are determined for the persistence of some of these periodic solutions after multivalued perturbations. Applications are given to dry friction problems.

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