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This paper deals with the existence of positive doubly periodic solutions for the nonlinear telegraph equation with delays ...u = f(t,x,u(t-τ1,x),..., u(t-τn,x)), (t,x) ∈ R², where ...u := utt - uxx + cut + a(t, x)u is a linear telegraph operator acting on function u: R²→R, c > 0 is a constant, a ∈ C(R², (0,∞)) is 2π-periodic in t and x,f ∈ C(R² × [0,∞)n, [0,∞)) is 2π-periodic in t and x, and τ1,..., τn ∈ [0,∞) are constants. Some existence results of positive doubly 2π-periodic weak solutions are obtained under that f (t, x,η1,...,ηn) satisfies some superlinear or sublinear growth conditions on η1,...,ηn. The discussion is based on the fixed point index theory in cones. [ABSTRACT FROM AUTHOR]

We discuss the existence of solution for the fully fourth-order boundary value problem u(4) = f(t, u, u', u'', u'''), 0 = t = 1, u(0) = u(1) = u''(0) = u''(1) = 0. A growth condition on f guaranteeing the existence of solution is presented. The discussion is based on the Fourier analysis method and Leray-Schauder fixed point theorem. [ABSTRACT FROM AUTHOR]

The existence of positive solutions for Neumann boundary value problem of second-order impulsive differential equations -u''(t) + Mu(t) = f(t, u(t), t ∊ J, t≠ tk, -?u'|t=tk = Ik(u(tk)), k = 1, 2, . . ., m, u'(0) = u'(1) = ?, in an ordered Banach space E was discussed by employing the fixed point index theory of condensing mapping, where M > 0 is a constant, J = [0, 1], f ∊ C(J×K,K), Ik ∊ C(K,K), k = 1, 2, . . ., m, andK is the cone of positive elements in E. Moreover, an application is given to illustrate the main result. [ABSTRACT FROM AUTHOR]

The existence results of positive solutions are obtained for the fourth-order periodic boundary value problem u(4) = βu" + αu = f(t, u, u"), 0 ≤ t ≤ 1, u(i)(0) = u(i)(1), i = 0, 1, 2, 3, where f : [0, 1] x ℝ+ x ℝ → ℝ+ is continuous, α, β ∈ ℝ, and satisfy 0 < α < ((β/2) + 2π&sup2:) &sup2:, β > -2 π², (α/ π4) + (β/π²) + 1 > 0. The discussion is based on the fixed point index theory in cones. [ABSTRACT FROM AUTHOR]

By means of the fixed point theory of strict set contraction operators, we establish a new existence theorem on multiple positive solutions to a singular boundary value problem for second-order impulsive differential equations with periodic boundary conditions in a Banach space. Moreover, an application is given to illustrate the main result. [ABSTRACT FROM AUTHOR]

In this article, we study the existence of piecewise-continuous mild solutions for the initial value problems for a class of semilinear evolution equations. These equations have non-instantaneous impulses in Banach spaces and the corresponding solution semigroup is noncompact. We assume that the nonlinear term satisfies certain local growth condition and a noncompactness measure condition. Also we assume the non-instantaneous impulsive functions satisfy some Lipschitz conditions. An example is given to illustrate our results. [ABSTRACT FROM AUTHOR]