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In this article, we investigate the asymptotic behavior of positive ground state solutions, as α → ∞, for the following Hénon type system -Δu = 2p/p+q|x|αup-1vq, -Δv = 2q/p+q|x|αupvq-1, in B1(0) with zero boundary condition, where B1(0) ⊂ ℝN (N ≥ 3) is the unit ball centered at the origin, p, q > 1, p + q < 2* = 2N/(N - 2). We show that both components of the ground solution pair (u, v) concentrate on the same point on the boundary ∂B1(0) as α → ∞. [ABSTRACT FROM AUTHOR]

By an application of Bonanno's three critical point theorem, we establish the existence of a nontrivial solution to the problem -Δpu = µg(x)|u|p-2u/|x|p + λa(x)f(u) in Ω, u = 0 on ∂Ω, under some restrictions on g, a and f for certain positive values of µ and λ. [ABSTRACT FROM AUTHOR]

This article concerns the solvability of the higher-order nonlinear neutral delay difference equation Δ(akn ... Δ(a2nΔ(a1nΔ(xn + bnxn-d)))) + s∑j = 1 pjnfj (xn-rjn) = qn, where n ≥ n0 ≥ 0, d, k, j, s are positive integers, fj : ℝ → ℝ and xfj (x) ≥ 0 for x ≠ 0. Sufficient conditions for the existence of non-oscillatory solutions are established by using Krasnoselskii fixed point theorem. Five theorems are stated according to the range of the sequence {bn}. [ABSTRACT FROM AUTHOR]

This paper presents a fixed point theorem of compression and expansion of functional type in the spirit of the original fixed point work of Leggett-Williams. Neither the entire lower nor the entire upper boundary is required to be mapped inward or outward. [ABSTRACT FROM AUTHOR]

In this article, we consider the third-order Sturm-Liouville boundary value problem, with p-Laplacian, (Φp(u"(t)))' + f(t, u(t)) = 0, t ∈ (0, 1), αu(0) - βu'(0) = 0, γ(1) + δu'(1) = 0, u"(0) = 0, where Φp(s) = |s|p-2s, p > 1. By means of the Leggett-Williams fixedpoint theorems, we prove the existence of multiple positive solutions. As an application, we give an example that illustrates our result. [ABSTRACT FROM AUTHOR]

This article concerns the existence of homoclinic solutions for the second order non-autonomous system q̈ + Aq̇ - L(t)q +Wq(t, q) = 0, where A is a skew-symmetric constant matrix, L(t) is a symmetric positive definite matrix depending continuously on t ∈ ℝ, W ∈ C¹(ℝ x ℝn,ℝ). We assume that W(t, q) satisfies the global Ambrosetti-Rabinowitz condition, that the norm of A is sufficiently small and that L and W satisfy additional hypotheses. We prove the existence of at least one nontrivial homoclinic solution, and the existence of infinitely many homoclinic solutions if W(t, q) is even in q. Recent results in the literature are generalized and improved. [ABSTRACT FROM AUTHOR]

In this work, we prove the existence and uniqueness of periodic solutions for a Liénard equation with two deviating arguments. Our main tools are the Mawhin's continuation theorem and the Schwarz inequality. We obtain our results under weaker conditions than those in, as shown by an example in the last section of this artticle. [ABSTRACT FROM AUTHOR]

We obtain a new oscillation theorem for the nonlinear secondorder differential equation (a(t)x'(t))' + p(t)f(t, x(t), x'(t)) + q(t)g(x(t)) = 0, t ∈ [0,∞), via the generalization of Leighton's variational theorem. [ABSTRACT FROM AUTHOR]

In this work, we consider the second order multi-point boundary-value problem with a p-Laplacian (ρ(t)Φp(x'(t)))' + f(t, x(t), x'(t)) = 0, t ∈ [0,+∞), x(0) = m ∑ i=1 αix(ξi), lim t→∞ x(t) = 0 . By applying a nonlinear alternative theorem, we establish existence and uniqueness of solutions on the half-line. Also a uniqueness result for positive solutions is discussed when f depends on the first-order derivative. The emphasis here is on the one dimensional p-Laplacian operator. [ABSTRACT FROM AUTHOR]

Neighborhoods of points in ℝn where a positive linear combination of C¹ vector fields sum to zero contain, generically, cyclic trajectories that switch between the vector fields. Such points are called stasis points, and the approximating switching cycle can be chosen so that the timing of the switches exactly matches the positive linear weighting. In the case of two vector fields, the stasis points form one-dimensional C¹ manifolds containing nearby families of two-cycles. The generic case of two flows in ℝ³ can be diffeomorphed to a standard form with cubic curves as trajectories. [ABSTRACT FROM AUTHOR]

We consider the uniqueness of solutions of ordinary differential equations where the coefficients may have singularities. We derive upper bounds on the order of singularities of the coefficients and provide examples to illustrate the results. [ABSTRACT FROM AUTHOR]

By using fixed-point theorem for operators on a cone, sufficient conditions for the existence of multiple positive solutions for a third-order boundary-value problem on the half-line are established. In the case of the p-Laplace operator our results for p > 1 generalize previous known results. The interesting point lies in the fact that the nonlinear term is allowed to depend on the first order derivative u'. [ABSTRACT FROM AUTHOR]

Using a fixed point theorem due to Avery and Peterson, this article shows the existence of solutions for multi-point boundary-value problem with p-Laplace operator and parameters. Also, we present an example to illustrate the results obtained. [ABSTRACT FROM AUTHOR]

By using Mawhin's continuation theorem of coincidence degree theory, we obtain sufficient conditions for the existence of positive almost periodic solutions for a non-autonomous delay competitive system with weak Allee effect. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of radial positive solutions for a nonpositone problem when the nonlinearity is superlinear and may have more than one zero. [ABSTRACT FROM AUTHOR]

We prove that solutions of the Cauchy problem for semilinear parabolic systems converge to solutions of the Cauchy problem for a corresponding systems of ordinary differential equations, as |x| → ∞. [ABSTRACT FROM AUTHOR]