[PDF] Top 20 Existence of Four Solutions of Some Nonlinear Hamiltonian System

... I and ˇ I of I on the submanifold with boundary C and ˇ C, respectively, and translate these two pairs of sphere-torus variational links of I and ˇ I into the two pairs of torus-sphere variational links of − I and − I, ... See full document

... By using critical point theory, we obtain some existence theorems of solutions for the nonlinear impulsive problem.. (.).[r] ... See full document

... It is well known that the iterative technique is a very important method for dealing with many nonlinear problems (see, e.g., [1–4]). Let E be a real Banach space, let X be a nonempty subset of E, and let A,B : X ... See full document

... the existence and multiplicity of various solutions of Hamiltonian ...on existence and multiplicity of peri- odic solutions, subharmonic solutions and homoclinic solutions ... See full document

... are some papers dealing with the existence of solutions (or positive solu- tions) of nonlinear fractional differential equation by the use of techniques of nonlinear analysis (fixed-point ... See full document

... the existence of positive solutions of a nonlinear second-order four- point boundary value problem with a p-Laplacian operator on time ...space. Existence result for p-Laplacian ... See full document

... From then on, the condition has been used extensively in the literature; see [–] and the references therein. In [], Fei also obtained the existence of nonconstant solutions for system (.) ... See full document

... 3. de Figueiredo, DG: Semilinear elliptic systems: a survey of superlinear problems. Resenhas 2, 373-391 (1996) 4. de Figueiredo, DG, Felmer, PL: On superquadratic elliptic systems. Trans. Am. Math. Soc. 343, 99-116 ... See full document

... Tas, Existence of radial positive solutions vanishing at infinity for asymptotically homogeneous systems, Electronic ...establish existence of nontrivial positive radial solution vanishing at infinity, ... See full document

... the existence and multiplicity of homoclinic solutions and periodic solutions for Hamiltonian systems have been extensively studied by critical point ...homoclinic solutions for the ... See full document

... Fourth-order nonlinear differential equations have many applications such as balancing condition of an elastic beam which may be described by nonlinear fourth-order ordinary differential ...the system ... See full document

... [16] B. Ahmad, J.J. Nieto, A. Alsaedi, M. El-Shahed, “A study of nonlinear Langevin equation involving two fractional orders in different intervals,” Nonlinear Anal. Real World Appl., vol.13, pp.599-606, ... See full document

... where S(n) is a real symmetric positive definite 2d × 2d matrix with S(n + p) = S(n) for every n ∈ Z , and then, for any real symmetric positive definite matrix S, we define a pair of index functions (i(S, p), ν(S, p)) ∈ ... See full document

... a Hamiltonian system is a system of differential equations which can model the motion of a mechanical ...the Hamiltonian system can support periodic ...and some other suitable ... See full document

... introduce some notations and lemmas needed in later ...the existence, uniqueness, stability, and continuity of solution p to the nonlinear equation ...the existence of weak solutions to ... See full document

... The nonlinear problems involving the p(t)-Laplace type operator are extremely attrac- tive because they can be used to model dynamical phenomena which arise from the study of elastic ...p(t)-Laplacian ... See full document

... of the Banach space, and we prove that the associated functional J of (.) satisfies the (P.S.) condition on the loop subspace D. In Section , we use a minimax method and critical point theory for the existence ... See full document

... which is a prototype of many problems. For more information, readers can refer to [37]. Because the energy functional corresponding to system (1.4) is unbounded from below, it is invalid to try finding a critical ... See full document

... the existence of the equilibrium solutions is established for the Volterra-Lotka mutualistic symbiosis model in the case of equal linear birth rates, using the method of upper and lower ... See full document

... The other significant difference between (.) and (.) is the corresponding optimal in- tegrable intervals of solutions. From (.), we know that the triplet (u, v, w) in (.) admits the same optimal integrable ... See full document