Existence of infinitely many brake orbits of Lagrangian autonomous systems on tori

Infinitely many monotone Lagrangian tori in del Pezzo surfaces

We construct almost toric fibrations (ATFs) on all del Pezzo surfaces, endowed with a monotone symplectic form. Except for CP2#CP2, CP2#2CP2, we are able to get almost toric base diagrams (ATBDs) of triangular shape and prove the existence of infinitely many symplectomorphism (in particular Hamiltonian isotopy) classes of monotone Lagrangian tori in CP2#kCP2 for k = 0, 3, 4, 5, 6, 7, 8. We name...

INFINITELY MANY HOMOCLINIC ORBITS OF SECOND-ORDER p-LAPLACIAN SYSTEMS

In this paper, we give several new sufficient conditions for the existence of infinitely many homoclinic orbits of the second-order ordinary p-Laplacian system d dt (|u̇(t)|p−2u̇(t)) − a(t)|u(t)|p−2u(t) +∇W (t, u(t)) = 0, where p > 1, t ∈ R, u ∈ R , a ∈ C(R,R) and W ∈ C(R × R ,R) are no periodic in t, which greatly improve the known results due to Rabinowitz and Willem.

Existence results of infinitely many solutions for a class of p(x)-biharmonic problems

The existence of infinitely many weak solutions for a Navier doubly eigenvalue boundary value problem involving the $p(x)$-biharmonic operator is established. In our main result, under an appropriate oscillating behavior of the nonlinearity and suitable assumptions on the variable exponent, a sequence of pairwise distinct solutions is obtained. Furthermore, some applications are pointed out.

Existence of infinitely many solutions for coupled system of Schrödinger-Maxwell's equations

Existence of Infinitely Many Elliptic Periodic Orbits in Four-Dimensional Symplectic Maps with a Homoclinic Tangency

We study the problem of coexistence of a countable number of periodic orbits of different topological types (saddles, saddle–centers, and elliptic) in the case of four-dimensional symplectic diffeomorphisms with a homoclinic trajectory to a saddle–focus fixed point.