In the article, we investigate three classes of fourth-order boundary value problems with dependence on all derivatives in nonlinearities under conditions involving Stieltjes integrals. A Gronwall-type inequality is employed to get an a priori bound third-order derivative term, and theory fixed-point index used suitable open sets obtain existence positive solutions. The have quadratic growth te...

In this paper using a fixed point theory on a cone we present some new results on the existence of multiple positive solutions for singular nonlocal boundary value problems involving integral conditions with derivative dependence.

In present paper, the author investigates the existence of positive solutions of boundaryvalue problems for second-order functional differential equations on infinite intervals as followsx′′ − p(t)x′ − q(t)x+ f(t, xt,xt) = 0, t ∈ I = [0,∞),αx(t)− βx′(t) = ξ(t) ≥ 0, t ∈ [−τ, 0], ξ(0) = x(∞) = 0,where α ≥ 0, β > 0, ξ(t) ∈ C[−τ, 0]. By applying fixed point index theorem on cone...

We discuss the existence of positive solutions for singular secondorder boundary value problems x′′ = μf (t, x, x′), ax(0) − bx′(0) = k ≥ 0, x′(∞) = 0, where f may be singular at x = 0 and x′ = 0 and can change sign. Via fixed point theory, we establish the existence of positive solutions under some conditions on f . Our results deal with the situation where the solutions approach the singulari...

In this paper, by using random fixed point index theory, some new boundary conditions based on strictly convex or strictly concave functions are established and some new theorems for the solutions of a class of random semi-closed 1-set-contractive operator equations A(ω, x) = μx are obtained, which extend and generalize some corresponding results of Wang [S. Wang, Fixed Point Theory Appl., 2011...

Bymeans of the fixed point index theory of strict-set contraction operator, we study the existence of positive solutions for the multipoint singular boundary value problem −1 n−ku n t f t, u t , 0 < t < 1, n ≥ 2, 1 ≤ k ≤ n−1, u 0 ∑m−2 i 1 aiu ξi , u i 0 u j 1 θ, 1 ≤ i ≤ k−1, 0 ≤ j ≤ n−k−1 in a real Banach space E, where θ is the zero element of E, 0 < ξ1 < ξ2 < · · · < ξm−2 < 1, ai ∈ 0, ∞ , i 1...

A class of elliptic boundary value problem in an exterior domain is considered under some conditions concerning the first eigenvalue of the relevant linear operator, where the variables of nonlinear term f(s, u) need not to be separated. Several new theorems on the existence and multiplicity of positive radial solutions are obtained by means of fixed point index theory. Our conclusions are esse...

In this article, by using the spectral analysis of the relevant linear operator and Gelfand’s formula, some properties of the first eigenvalue of a fractional differential equation are obtained. Based on these properties and through the fixed point index theory, the singular nonlinear fractional differential equations with Riemann–Stieltjes integral boundary conditions involving fractional deri...