Critical Point Theory and Hamiltonian Systems

Mawhin, Jean; Willem, Michel

doi:10.1007/978-1-4757-2061-7

Cited by 1,673 publications

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“…The idea behind them is trying to find solutions of a given boundary value problem by looking for critical points of a suitable energy functional defined on an appropriate function space. In the last 30 years, the critical point theory has become to a wonderful tool in studying the existence of solutions to differential equations with variational structures, we refer the reader to the books due to Mawhin and Willem [24], Rabinowitz [29] and the references listed therein.…”

mentioning

confidence: 99%

Existence of three solution for fractional Hamiltonian system

Ledesma¹,

Diestra²

2017

Sel.mat

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Resumen En este artículo se considera un sistema Hamiltoniano dado por (t)) = ∇F (t, u(t)), a.e t ∈ [0, T ] (0.1)u(0) = u(T ) = 0. Abstract In this paper we consider the fractional Hamiltonian system given bywhere Keywords. Fractional calculus, fractional derivatives, fractional Hamiltonian system, boundary value problem ------------------------ Introduction.Fractional order models can be found to be more adequate than integer order models in some real world problems as fractional derivatives provide an excellent tool for the description of memory and hereditary properties of various materials and processes. The mathematical modeling of systems and processes in the fields of physics, chemistry, aerodynamics, electro dynamics of complex medium, polymer rheology, etc. involves derivatives of fractional order. As a consequence, the subject of fractional differential equations is gaining more importance and attention. There has been significant development in ordinary and partial differential equations involving both Riemann-Liouville and Caputo fractional derivatives.

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mentioning

confidence: 99%

Existence of three solution for fractional Hamiltonian system

Ledesma¹,

Diestra²

2017

Sel.mat

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“…Critical point theory has been very useful in determining the existence of solution for integer order differential equations with some boundary conditions, for example [11,35,38,45]. But until now, there are few results on the solution to fractional boundary value problems which were established by the critical point theory, since it is often very difficult to establish a suitable space and variational functional for fractional boundary value problems.…”

Section: U(t)) + A(t)u(t) = λF (T U(t)) + H(u(t)) T = Tmentioning

confidence: 99%

Existence of three solutions for impulsive nonlinear fractional boundary value problems

Heidarkhani

Феррара

Caristi

et al. 2017

OpMath

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“…One set consists of solutions with negative energy, while the other set contains solutions with arbitrary energy. We briefly recall here some background facts that we will use in the sequel [20,21,24,26]. Let…”

Section: Infinitely Many Solutionsmentioning

confidence: 99%

“…Let N be a closed neighborhood of K c in S such that γ(N) = γ(K c ). The deformation lemma [21,24,26,28] ensures the existence of an odd homeomorphism Φ from S to S and ε > 0 such that Notice that λ ≤ λ * . An interesting question is to compare α(λ) (resp., α(λ)) with E λ (c(λ)) (resp., with E λ (c(λ))).…”

Section: Infinitely Many Solutionsmentioning

confidence: 99%

Multiple solutions to a nonlinear elliptic equation involving Paneitz type operators

Hamidi

2004

International Journal of Mathematics and Mathematical Sciences

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Introduction.In this paper, we study a nonlinear elliptic equation involving Paneitz type operators on compact Riemannian manifolds. The nonlinearity considered here is concave-convex. The simultaneous effect of the concave and convex terms has been initially investigated by Ambrosetti et al. [1] in the Euclidian case for the Laplace operator. Since then, elliptic problems with this kind of nonlinearities were extensively studied by several authors with different classes of domains and with more general differential operators like the p-Laplacian. We can refer the reader to the valuable survey article by Ambrosetti et al. [2] and the references therein.The aim of this paper is to establish nonlocal and multiple existence results (with respect to a real parameter) to an elliptic equation involving the Paneitz-Branson operator with concave-convex nonlinear terms. Also, characteristic values of the real parameter are introduced (under variational form) and some of their specific properties are carried out. Now, let (M, g) be a smooth 4-dimensional Riemannian manifold and let S g , Rc g be the scalar curvature and the Ricci curvature of g, respectively. The Paneitz operator, introduced by Paneitz [23], defined on (M, g) is the fourth-order operator

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Critical Point Theory and Hamiltonian Systems

Cited by 1,673 publications

References 0 publications

Existence of three solution for fractional Hamiltonian system

Existence of three solution for fractional Hamiltonian system

Existence of three solutions for impulsive nonlinear fractional boundary value problems

Multiple solutions to a nonlinear elliptic equation involving Paneitz type operators

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