On the existence of infinitely many periodic solutions for an equation of a rectangular thin plate
On the existence of periodic solutions of a semilinear wave equation with a superlinear forcing term
On the existence of periodic solutions of an hyperbolic equation in a thin domain
For a nonlinear hyperbolic equation defined in a thin domain we prove the existence of a periodic solution with respect to time both in the non-autonomous and autonomous cases. The methods employed are a combination of those developed by J. K. Hale and G. Raugel and the theory of the topological degree.
On the existence of positive solutions for periodic parabolic sublinear problems.
On the existence of two-dimensional invariant tori for scalar parabolic equations with time periodic coefficients
On the instability of a class of periodic travelling wave solutions of the modified Boussinesq equation.
On the long time behaviour of solutions of a class of autonomous reaction-diffusion systems.
On the solvability of a system of wave and beam equations.
On the time periodic free boundary associated to some nonlinear parabolic equations.
On the weakly nonlinear wave equation involving a small parameter at the highest derivative
On unique solvability of the periodic problem in the plane for linear hyperbolic equations.
One-dimensional symmetry of periodic minimizers for a mean field equation
We consider on a two-dimensional flat torus defined by a rectangular periodic cell the following equationIt is well-known that the associated energy functional admits a minimizer for each . The present paper shows that these minimizers depend actually only on one variable. As a consequence, setting to be the first eigenvalue of the Laplacian on the torus, the minimizers are identically zero whenever . Our results hold more generally for solutions that are Steiner symmetric, up to a translation....
Oscillatory and periodic solutions to a diffusion equation of neutral type.