Multiple Periodic Solutions for Perturbed Second-Order Impulsive Hamiltonian Systems

Graef, John R.; Heidarkhani, Shapour; Kong, Lingju

doi:10.12732/ijpam.v109i1.7

Cited by 6 publications

(3 citation statements)

References 44 publications

(49 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, by adopting the same hypotheses on the potential and in presence of suitable small perturbations, the same conclusion is achieved. We refer to [7,[27][28][29][30][31]33] in which existence results for BVPs employing Ricceri's variational principle and its variants were established.…”

Section: Introductionmentioning

confidence: 99%

Existence and multiplicity of weak solutions for gradient-type systems wıth oscillatory nonlinearities on the sierpinski gasket

Alrikabi¹,

Afrouzi²,

Alimohammady³

2018

HJMS

View full text Add to dashboard Cite

In this paper, we establish the existence and multiplicity results of solutions for parametric quasi-linear systems of the gradient-type on the Sierpiński gasket is proved. Our technical approach is based on variational methods and critical points theory and on certain analytic and geometrical properties of the Sierpiński fractal. Indeed, using a consequence of the local minimum theorem due to Bonanno, the Palais-Smale condition cut off upper at r, and the Palais-Smale condition for the Euler functional we investigate the existence of one and two solutions for our problem under algebraic conditions on the nonlinear part. Moreover by applying a different three critical point theorem due to Bonanno and Marano we guarantee the existence of third solution for our problem.

show abstract

Section: Introductionmentioning

confidence: 99%

Existence and multiplicity of weak solutions for gradient-type systems wıth oscillatory nonlinearities on the sierpinski gasket

Alrikabi¹,

Afrouzi²,

Alimohammady³

2018

HJMS

View full text Add to dashboard Cite

show abstract

“…For more details on Theorem 2.1, we refer the readers to [17,18], where the theorem has already been applied to nonlinear secondorder differential equations problems. We also refer to [19,20,21] in which, Theorems 2.1 and 2.2 along with the mountain pass theorem have been successfully employed to ensure multiple solutions for some boundary value problems. We also refer the reader to the papers [22,23] in which based on variational methods and critical point theory, the existence of multiple solutions for boundary value problems was discussed.…”

Section: Introductionmentioning

confidence: 99%

Existence results for a class of second order differential equations with nonlinear derivative dependence

2018

J. Nonlinear Funct. Anal.

View full text Add to dashboard Cite

We establish multiplicity results for nontrivial solutions of the quasilinear second order differential equation on afor 1 ≤ i ≤ n, under appropriate hypotheses. Indeed, using a consequence of the local minimum theorem due to Bonanno and, the mountain pass theorem, we investigate the existence of two solutions for the problem under some algebraic conditions with the classical Ambrosett-Rabinowitz condition on the nonlinear terms. Moreover, by combining two algebraic conditions on the nonlinear terms, and employing two consequences of the local minimum theorem due to Bonanno, we guarantee the existence of two solutions for the scalar case of the problem. Applying the mountain pass theorem given by Pucci and Serrin, we ensure the existence of the third solution for our problem.

show abstract

“…In [11,18,19,24] using variational methods and critical point theory the existence of multiple solutions for a class of perturbed second-order impulsive Hamiltonian systems was discussed.…”

Section: Introductionmentioning

confidence: 99%

Multiple solutions for a class of perturbed damped vibration problems

Tavani¹,

Afrouzi²,

Heidarkhani³

2016

J. Math. Computer Sci.

View full text Add to dashboard Cite

show abstract

Multiple Periodic Solutions for Perturbed Second-Order Impulsive Hamiltonian Systems

Abstract: The existence of three distinct periodic solutions for a class of perturbed impulsive Hamiltonian systems is established. The techniques used in the proofs are based on variational methods.

Cited by 6 publications

References 44 publications

Existence and multiplicity of weak solutions for gradient-type systems wıth oscillatory nonlinearities on the sierpinski gasket

Existence and multiplicity of weak solutions for gradient-type systems wıth oscillatory nonlinearities on the sierpinski gasket

Existence results for a class of second order differential equations with nonlinear derivative dependence

Multiple solutions for a class of perturbed damped vibration problems

Contact Info

Product

Resources

About