We investigate the existence and multiplicity of homoclinic orbits for second-order Hamiltonian systems with local superquadratic potential by using the Mountain Pass Theorem and the Fountain Theorem, respectively.
This paper is concerned with the existence of homoclinic solutions for a class of the second order impulsive Hamiltonian systems. By employing the Mountain Pass Theorem, we demonstrate that the limit of a2kT-periodic approximation solution is a homoclinic solution of our problem.
AbstractBy using the variant version of Mountain Pass Theorem, the existence of homoclinic solutions for a class of second-order Hamiltonian systems is obtained. The result obtained generalizes and improves some known works.
This paper is concerned with the following nonlinear second-order nonautonomous problem:ü(t)+q(t)u̇(t)-∇K(t,u(t))+∇W(t,u(t))=0, wheret∈R,u∈RN, andK,W∈C1(R×RN,R)are not periodic intandq:R→Ris a continuous function andQ(t)=∫0tq(s)dswithlim|t|→+∞Q(t)=+∞. The existence and multiplicity of fast homoclinic solutions are established by using Mountain Pass Theorem and Symmetric Mountain Pass Theorem in critical point theory.
By using the symmetric mountain pass theorem, we establish some new existence criteria to guarantee that the second-order Hamiltonian systems ü(t) − L(t)u(t) + ∇W(t,u(t)) = 0 have infinitely many homoclinic orbits, where t ∈ ℝ, u ∈ ℝN, L ∈ C(ℝ, ℝN × N) and W ∈ C1(ℝ × ℝN, ℝ) are not periodic in t. Our results generalize and improve some existing results in the literature by relaxing the conditions on the potential function W(t, x).
AbstractIn this paper we study impulsive periodic solutions for second-order nonautonomous singular differential equations. Our proof is based on the mountain pass theorem. Some recent results in the literature are extended.
Existence and Multiplicity of Homoclinic Orbits for Second-Order Hamiltonian Systems with Superquadratic Potential
