Multiple solutions of the forced double pendulum equation
A survey of recent progress on the multiplicity and stability problems for closed geodesics on Finsler 2-spheres is given.
We prove the existence of infinitely many geometrically distinct homoclinic orbits for a class of asymptotically periodic second order Hamiltonian systems.
We discuss the existence and multiplicity of positive solutions for a class of second order quasilinear equations. To obtain our results we will use the Ekeland variational principle and the Mountain Pass Theorem.
In this paper, we consider the problem of multiplicity of conformal metrics of prescribed scalar curvature on standard spheres . Under generic conditions we establish someMorse Inequalities at Infinity, which give a lower bound on the number of solutions to the above problem in terms of the total contribution of its critical points at Infinityto the difference of topology between the level sets of the associated Euler-Lagrange functional. As a by-product of our arguments we derive a new existence...