Transversal homoclinics in nonlinear systems of ordinary differential equations.
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.
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