This paper is concerned with the existence and multiplicity of fast homoclinic solutions for a class of damped vibration problems with impulsive effects. Some new results are obtained under more relaxed conditions by using Mountain Pass Theorem and Symmetric Mountain Pass Theorem in critical point theory. The results obtained in this paper generalize and improve some existing works in the literature.
By using mountain pass theorem and local link theorem, some existence theorems are obtained for periodic solutions of second order non-autonomous Hamiltonian systems under local superquadratic condition and other suitable conditions.
ABSTRACT. By 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.
In this paper, we intend to study the following Klein‐Gordon‐Maxwell system:
−normalΔu+false(λAfalse(xfalse)+1false)u−false(2ω+φfalse)φu=ffalse(ufalse),1emx∈ℝ3,normalΔφ=false(ω+φfalse)u2,1emx∈ℝ3.
By adopting some new analytical skills and employing variational methods, the existence of a ground state solution for the above system is established under suitable conditions on A and f. The range of ω is more wider than Liu et al., Theorem 1.1
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