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In this paper, we investigate a set-valued solution of the following Pexider functional equation F(ax + by) = ΑG(x) + βH(y) with three unknown functions F, G and H, where a, b, Α β are positive real scalars. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the existence of positive solutions of the fully third-order boundary value problem... is continuous. Some inequality conditions on f to guarantee the existence of positive solution are presented. These inequality conditions allow that ƒ(t; x; y; z) may be superlinear or sublinear growth on x, y and z as |(x; y; z)| → 0 and |(x; y; z)| → ∞. [ABSTRACT FROM AUTHOR]

In this paper, we first establish a new fixed point theorem in cones of Banach spaces. Then, we apply the fixed point theorem to study the existence and uniqueness of monotone positive solutions for an elastic beam equation u(4)(t) = f(t; u(t); u'(t)) with superlinear boundary conditions. An example is given to illustrate our main result. Compared with some earlier results (cf. [10]), the biggest differences are that we consider such equation with superlinear boundary conditions and remove some restrictive conditions. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the existence of positive solutions of the fully third-order boundary value problem ..., where f: [0, 1] x ℝ+ x ℝ+ x ℝ → ℝ is continuous. Some inequality conditions on f to guarantee the existence of positive solution are presented. These inequality conditions allow that f (t, x, y, z) may be superlinear or sublinear growth on x, y and z as |(x, y, z)| → 0 and |(x, y, z)| → ∞. [ABSTRACT FROM AUTHOR]

In this paper, we first establish a new fixed point theorem in cones of Banach spaces. Then, we apply the fixed point theorem to study the existence and uniqueness of monotone positive solutions for an elastic beam equation u(4)(t) = f(t,u(t),u'(t)) with superlinear boundary conditions. An example is given to illustrate our main result. Compared with some earlier results (cf. [10]), the biggest differences are that we consider such equation with superlinear boundary conditions and remove some restrictive conditions. [ABSTRACT FROM AUTHOR]

In this paper, we define the following additive set-valued functional equation f(2x+3y-z)+f(2y+3z-x)+f(3x+2z-y) =f(x+y)+f(y+z)+f(x+z)+f(2x)+f(2y)+f(2x)and prove the Hyers-Ulam stability of the above additive set-valued functional equaition. [ABSTRACT FROM AUTHOR]

This paper is concerned with a class of boundary value problems for the nonlinear mixed impulsive integro-differential equations with the derivative u 1 and deviating arguments in Banach space by using the cone theory and upper and lower solutions method together with monotone iterative technique. Sufficient conditions are established for the existence of extremal solutions of the given problem. [ABSTRACT FROM AUTHOR]

This paper is concerned with a class of boundary value problems for the nonlinear mixed impulsive integro-differential equations with the derivative u and deviating arguments in Banach space by using the cone theory and upper and lower solutions method together with monotone iterative technique. Sufficient conditions are established for the existence of extremal solutions of the given problem. [ABSTRACT FROM AUTHOR]

In this paper, we consider the multipoint boundary value problem for the one-dimensional p-Laplacian system { (ϕp1 (u1))1 + q1(t)f(t, u, v) = 0; t ϵ (0, 1), (ϕp2 (u1))1 + q2(t)f(t, u, v) = 0; t ϵ (0, 1), { u(0) = ∑m-2 i=1 aiu(ξi); u1(1) = Bu1(0), { u(0) = ∑m-2 i=1 aiu(ξi); u1(1) = Bu1(0), where ϕpi (s) = ∣s∣pi-2s, pi > 1, i = 1, 2, ξi ϵ (0, 1) with 0 < ξ1 < ξ2 < ... < ξ m-2 < 1 and ɑi ϵ [0, 1), ∑m-2 i=1 ɑi < 1; β ϵ (0; 1). By using the fixed point index theorem on cones, we study the existence of positive solutions for the m-point boundary value problem with sign changing nonlinear term. Some sufficient conditions for the exis- tence of multiple positive solutions are obtained. Finally, an example is also included to illustrate the importance of the main result obtained. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of positive solutions to the differencesummation boundary value problem... where f is continuous, T ≥ 5 is a fixed positive integer, η ∈ {4, 5, ..., T - 1},... . We show the existence of at least one positive solution if f is either superlinear or sublinear by applying Guo-Krasnoselskii fixed point theorem in cones. [ABSTRACT FROM AUTHOR]

In this paper, we consider the multipoint boundary value problem for the one-dimensional p-Laplacian system (ϕp1 (u'))' + q1(t)f(t; u; v) = 0; t ∊ (0; 1); (ϕp2 (v'))' + q2(t)g(t; u; v) = 0; t ∊ (0; 1); u(0) = Σm-2i=1 aiu(ξi); u'(1) = βuμi(0); v(0) = m- 2i=1 ai v(ξi); v'(1) = βv'(0); where ϕpi (s) = ∣s∣pi-2s, pi > 1; i = 1; 2; ξi ∊ (0; 1) with 0 < ξ1 < ξ2 < ... < ξm-2 < 1 and ai ∊ [0; 1); Σm- 2i=1 ai < 1; β ∊ (0; 1). By using the fixed point index theorem on cones, we study the existence of positive solutions for the m-point boundary value problem with sign changing nonlinear term. Some sufficient conditions for the existence of multiple positive solutions are obtained. Finally, an example is also included to illustrate the importance of the main result obtained. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of positive solutions to the differencesummation boundary value problem Δ4u(t - 2) + a(t)f(u) = 0, t ∊ {2, 3, ..., T}, u(0) = Δu(0) = Δ2u(0) = 0, u(T + 2) = α Ση s=4 u(s), where f is continuous, T ≥ 5 is a fixed positive integer, η ∊ {4, 5, ..., T - 1}, 0 < α < 4T(T+1)(T+2)/(η-3)(η+2)(η2-η+4). We show the existence of at least one positive solution if f is either superlinear or sublinear by applying Guo-Krasnoselskii fixed point theorem in cones. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of positive solutions to the difference-summation boundary value problem Δ²u(t - 1) + a(t) f(u) = 0, t ∈ {1, 2, ..., T}, u(0) = βΔu(0), ... where f is continuous, T ≥ 3 is a fixed positive integer, η ∈ {1,2, ...,T - 1}, 0 < α < 2(T-1)/η(η+1), 0 < β < 2(T+1) - αη(η+1)/2(αη-1) and Δu(t - 1) = u(t) - u(t - 1). We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem due to Krasnoselskii in cones. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of positive solutions to the differencesummation boundary value problem ... , where f is continuous, T = 3 is a fixed positive integer, ... and .... We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem due to Krasnoselskii in cones. [ABSTRACT FROM AUTHOR]

In this paper, we consider a 2nth-order boundary value problem for dynamic equations on time scales. We establish criteria for the existence of one or more positive solutions by using fixed point theorem of cone expansion and compression type. We also give an example to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a 2nth-order boundary value problem for dynamic equations on time scales. We establish criteria for the existence of one or more positive solutions by using fixed point theorem of cone expansion and compression type. We also give an example to illustrate our results. [ABSTRACT FROM AUTHOR]