New exact solutions for the -dimensional Broer-Kaup-Kupershmidt equations.
Nonlinear models of suspension bridges: discussion of the results
In this paper we present several nonlinear models of suspension bridges; most of them have been introduced by Lazer and McKenna. We discuss some results which were obtained by the authors and other mathematicians for the boundary value problems and initial boundary value problems. Our intention is to point out the character of these results and to show which mathematical methods were used to prove them instead of giving precise proofs and statements.
Nonlinear vibrations of completely resonant wave equations
We present recent existence results of small amplitude periodic and quasi-periodic solutions of completely resonant nonlinear wave equations. Both infinite-dimensional bifurcation phenomena and small divisors difficulties occur. The proofs rely on bifurcation theory, Nash-Moser implicit function theorems, dynamical systems techniques and variational methods.
Nonlocal Robin problem for elliptic second order equations in a plane domain with a boundary corner point
We investigate the behavior of weak solutions to the nonlocal Robin problem for linear elliptic divergence second order equations in a neighborhood of a boundary corner point. We find an exponent of the solution's decreasing rate under minimal assumptions on the problem coefficients.
Note to periodic solvability of the boundary value problem for nonlinear heat equation