Transversal homoclinics in nonlinear systems of ordinary differential equations.
Bifurcation of multi-bump homoclinics in systems with normal and slow variables.
Some remarks on the Melnikov function.
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
Nontrivial critical points of asymptotically quadratic functions at resonances
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.
Critical points of asymptotically quadratic functions
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.
Note on weakly inward mappings
The Nielsen fixed point theory is used to show several results for certain operator equations involving weakly inward mappings.
Semilinear problems with nonlinearities depending only on derivatives
A certain type of partial differential equations on tori
The existence of classical solutions for some partial differential equations on tori is shown.
Bifurcation of heteroclinic orbits for diffeomorphisms
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.
On the existence of chaotic behaviour of diffeomorphisms
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.
Invariant curves from symmetry
We show that certain symmetries of maps imply the existence of their invariant curves.
Periodically forced damped beams resting on nonlinear elastic bearings
Periodic orbits of certain Hénon-like maps
The relation between a flow and its discretization
Note on a local invertibility
Periodic solutions in systems at resonances with small relay hysteresis
Note on a Poincaré map
On a theorem of L. Lefton
Existence results for implicit differential equations
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