Iterative technique for third-order differential equation with three-point nonlinear boundary value conditions

In this paper, we study the existence of extremal solutions for a nonlinear third-order differential equation with three-point nonlinear boundary value conditions. By means of the method of upper and lower solutions and different monotone iterative techniques, the sufficient conditions which guarantee the existence of extremal solutions are given. An example illustrates the main results

On a fixed point theorem of mixed monotone operators and applications

In this paper, by introducing $\tau-\varphi-$ mixed monotone operators in ordered Banach spaces, the existence and uniqueness theorems for the operators are obtained. In the end, the new results are used to study the existence of positive solutions to second order equations with Neumann boundary conditions

On existence and uniqueness of positive solutions for integral boundary boundary value problems

By applying the monotone iterative technique, we obtain the existence and uniqueness of $C^1[0,1]$ positive solutions in some set for singular boundary value problems of second order ordinary differential equations with integral boundary conditions

Triple positive solutions for semipositone fractional differential equations m-point boundary value problems with singularities and p–q-order derivatives

In this paper, by means of Leggett–Williams and Guo–Krasnosel'skii fixed point theorems, together with height functions of the nonlinearity on different bounded sets, triple positive solutions are obtained for some fractional differential equations with p–q-order derivatives involved in multi-point boundary value conditions. The nonlinearity may not only take negative infinity but also may permit singularities on both the time and the space variables

On the Existence of Solutions for Impulsive Fractional Differential Equations

We are concerned with a type of impulsive fractional differential equations attached with integral boundary conditions and get the existence of at least one positive solution via global bifurcation techniques

Mechanism of differential Zika and dengue virus neutralization by a public antibody lineage targeting the DIII lateral ridge

We previously generated a panel of human monoclonal antibodies (mAbs) against Zika virus (ZIKV) and identified one, ZIKV-116, that shares germline usage with mAbs identified in multiple donors. Here we show that ZIKV-116 interferes with ZIKV infection at a post-cellular attachment step by blocking viral fusion with host membranes. ZIKV-116 recognizes the lateral ridge of envelope protein domain III, with one critical residue varying between the Asian and African strains responsible for differential binding affinity and neutralization potency (E393D). ZIKV-116 also binds to and cross-neutralizes some dengue virus serotype 1 (DENV1) strains, with genotype-dependent inhibition explained by variation in a domain II residue (R204K) that potentially modulates exposure of the distally located, partially cryptic epitope. The V-J reverted germline configuration of ZIKV-116 preferentially binds to and neutralizes an Asian ZIKV strain, suggesting that this epitope may optimally induce related B cell clonotypes. Overall, these studies provide a structural and molecular mechanism for a cross-reactive mAb that uniquely neutralizes ZIKV and DENV1

Positive solutions for singular three-point boundary-value problems

In this paper, we present the Green's functions for a second-order linear differential equation with three-point boundary conditions. We give exact expressions of the solutions for the linear three-point boundary problems by the Green's functions. As applications, we study uniqueness and iteration of the solutions for a nonlinear singular second-order three-point boundary value problem