[PDF] Top 20 Homoclinic Solutions of Singular Nonautonomous Second-Order Differential Equations

... is investigated under the assumptions that f is continuous, it has three distinct zeros and satisfies the sign conditions similar to those in 11, 3.4. In 13, an approach quite different from 11, 12 is used. In particular, ... See full document

... Our approach combines phase-plane analysis with time-mapping estimates. As in [, , , , , ], the solutions are obtained by connecting the unstable and stable manifolds of the equilibrium points of the ... See full document

... 5. Application. In this section, we present a few examples of the applica- tions of Theorem 4.2 and other results of this paper. We are going to study the effect of some second-order terms on (2.4). For this ... See full document

... where a min{0, inf{τ t : 0 ≤ t ≤ 1}}, b max{1, sup{τt : 0 ≤ t ≤ 1}}, and the existence of positive solutions to 1.1 is obtained. When τt t − r in 1.1, Agarwal and O’Regan in 5, Lin and Xu in 6 discussed the ... See full document

... of homoclinic solutions for im- pulsive differential equations by using perturbation ...of homoclinic solutions for Hamiltonian systems via variational ...of solutions of ... See full document

... has exactly k zeros in (a,b), it is possible to obtain the asymptotic distribution of eigen- values from the asymptotic number of zeros of solutions, an idea which goes back at least to Hartman (see [3]). For the ... See full document

... periodic solutions do not ...periodic solutions under the presence of a weak singularity by topological methods is more recent but has also attracted many researchers 4, 6, ...lower solutions 6, 29, ... See full document

... of singular impulsive differential equations has been emerging as an important area of investigation in recent ...a second-order differential equation u ft, u, u , one usually considers impulses ... See full document

... differential equations has been emerging as an important area of investigation in recent years (see ...differential equations, impulsive functional differential equations and impulsive differential ...of ... See full document

... of solutions in these ...and homoclinic solutions for a class of second-order differential equations of the form () in the case μ = , via variational methods, the results ... See full document

... periodic solutions to ordinary differential systems as well as partial differential equa- tions (see ...periodic solutions for delay differential ...periodic solutions for the func- tional differential ... See full document

... To illustrate the solution behaviour, described by Theorems 3.3 and 3.5, we have carried out a series of numerical calculations on a MATLAB software package bvpsuite designed to solve boundary value problems in ordinary ... See full document

... classical solutions of the nonau- tonomous second-order equation: u (t) = A(t)u (t)+B(t)u(t)+f (t), 0 ≤ t ≤T ; u(0) =x 0 , u (0) = x 1 on a Banach space by means of operator matrix method and apply ... See full document

... second-order nonlinear damped differential equations by combing the analysis of positiveness of the Green function for a linear damped equation. Our nonlinearity may be singular in its ... See full document

... periodic solutions to second order differential equations with singular nonlinear ...positive solutions under reasonable ... See full document

... (.) is bounded from below, techniques based on the genus properties have been well applied. In particular, Clark’s theorem is an effective tool to prove the existence and mul- tiplicity of homoclinic ... See full document

... The periodic problem (1.1) was studied by Mawhin and Willem [7, 8], Long [5], Tang and Wu [13–15] and others (cf. the refernces quoted in them). Ben-Naoum et al. [2] and Nirenberg (cf. Ekeland and Ghoussoub [4]) proved ... See full document

... and asymptotic formulas can be established. In contrast to the linear case, a reduction of order formula is not at our disposal. A topic which would also be of interest is to obtain more precise information as ... See full document

... The paper is organized as follows. In Section 2, we give some lemmas, which will be required in the proof of our main theorem. In Section 3, we prove some theorems on the existence of positive solutions for BVP ... See full document

... 6 1969, 365-374 [8] NA, T.Y., Computanonal Methods in Engineering Boundary Value Problems, Academic Press, New York 1979 [9] SHAW, R.E and GAREY, L.E., Monotonic approximations for nonli[r] ... See full document