Daniel Paşca

Some existence results on periodic solutions of nonautonomous second-order differential systems with (q,p)-Laplacian

Abstract Some existence theorems are obtained for periodic solutions of nonautonomous second-order differential systems with ( q , p ) -Laplacian by using the least action principle and the minimax methods.

Infinitely many periodic solutions for a class of new superquadratic second-order Hamiltonian systems☆

Abstract In this paper, we establish the existence of infinitely many periodic solutions for a class of new superquadratic second-order Hamiltonian systems. Our technique is based on the Fountain Theorem due to Bartsch.

Periodic solutions of non-autonomous second order systems with (q(t), p(t))-Laplacian

Using the least action principle in critical point theory we obtain some existence results of periodic solutions for (q(t), p(t))-Laplacian systems which generalize some existence results.

Escape dynamics in collinear atomic-like three mass point systems

Abstract The present paper studies the escape mechanism in collinear three point mass systems with small-range-repulsive/large-range-attractive pairwise interaction. Specifically, we focus on the asymptotic behaviour for systems with non-negative total energy. On the zero energy level set there are two distinct asymptotic states, called 1 + 1 + 1 escape configurations, where all the three separations infinitely increase as t → ∞ . We show that 1 + 1 + 1 escapes are improbable by proving that the set of initial conditions leading to such asymptotic configurations has zero Lebesgue measure. When the outer mass points are of the same kind we deduce the existence of a heteroclinic orbit connecting the 1 + 1 + 1 escape configurations. We further prove that this orbit is stable under parameter perturbation. In the positive energies’ case, we show that the set of initial conditions leading to 1 + 1 + 1 escape configurations has positive Lebesgue measure.

Homoclinic solutions for ordinary (q, p)-Laplacian systems with a coercive potential

Abstract A result for the existence of homoclinic orbits is obtained for (q, p)-Laplacian systems.

Qualitative analysis of the anisotropic two-body problem with relativistic potential

In this paper we study the two-body problem that describes the motion of two-point masses in an anisotropic space under the influence of a Newtonian force-law with two relativistic correction terms. We will show that the set of initial conditions leading to collisions and ejections have positive measure and study the capture and escape solutions in the zero-energy case using the infinity manifold. We will also apply the Melnikov method to show that the flow on the zero-energy manifold of another potential which is the sum of the classical Keplerian potential and two anisotropic perturbation which also take into account two relativistic correction terms is chaotic.

Periodic Solutions of Superlinear Convex Autonomous Hamiltonian Systems

Using the Szulkins variant of Mountain Pass Theorem, we prove the existence of nontrivial orbits with prescribed period for autonomous Hamiltonian systems in infinite dimen-sional Hilbert spaces.