Positive solvability of systems of nonlinear Hammerstein integral equations

The paper deals with the existence of positive continuous solutions to systems of nonlinear Hammerstein integral equations. The main tool used in the proofs is fixed point index theory in a cone. The results obtained here are essentially different from existing ones in the literature.     

A ketogenic diet as a potential novel therapeutic intervention in amyotrophic lateral sclerosis

Background  

The cause of neuronal death in amyotrophic lateral sclerosis (ALS) is uncertain but mitochondrial dysfunction may play an important role. Ketones promote mitochondrial energy production and membrane stabilization.     

Existence of positive solutions for singular ordinary differential equations with nonlinear boundary conditions

We prove the existence of nonnegative solutions of the problem , , for a physically motivated class of nonlinearity . The results, which are established using a ``forbidden value' argument, are new even in the case of linear .

     

Regularization of a final value problem for a nonlinear biharmonic equation

In this paper, we consider the nonlinear biharmonic equation. The problem is ill‐posed in the sense of Hadamard. To obtain a stable numerical solution, we consider a regularization method. We show rigourously, with error estimates provided, that the corresponding regularized solutions converge to the true solution strongly in uniformly with respect to the space coordinate under some a priori assumptions on the solution.     

Anti-periodic solutions for evolution equations associated with maximal monotone mappings

In this work, we study the anti-periodic problem for a nonlinear evolution inclusion where the nonlinear part is an odd maximal monotone mapping and the forcing term is an anti-periodic mapping. Several existence results are obtained under suitable conditions. An example is presented to illustrate the results.     

A uniqueness criterion for fractional differential equations with Caputo derivative

We investigate the uniqueness of solutions to an initial value problem associated with a nonlinear fractional differential equation of order α∈(0,1). The differential operator is of Caputo type whereas the nonlinearity cannot be expressed as a Lipschitz function. Instead, the Riemann–Liouville derivative of this nonlinearity verifies a special inequality.     

Existence of positive solutions to time scale equations using time scale inequalities ∗

Krasnoselskii’s fixed point theorem and time scale inequalities are used to establish the existence of positive solutions to some time scale equations     

Continuums of solutions for integral inclusions on the half line

In this paper we show that the solution set of certain Volterra inclusions on the half line is a continuum.