A minimax inequality and its applications to ordinary differential equations

A Generalized Wirtinger’s Inequality with Applications to a Class of Ordinary Differential Equations

We first prove a generalized Wirtinger’s inequality. Then, applying the inequality, we study estimates for lower bounds of periods of periodic solutions for a class of delay differential equations ẋ t −∑nk 1f x t − kr , and ẋ t − ∑n k 1g t, x t − ks , where x ∈ R, f ∈ C R,R , and g ∈ C R×Rp,Rp and r > 0, s > 0 are two given constants. Under some suitable conditions on f and g, lower bounds of p...

APPLICATION NEURAL NETWORK TO SOLVE ORDINARY DIFFERENTIAL EQUATIONS

In this paper, we introduce a hybrid approach based on neural network and optimization teqnique to solve ordinary differential equation. In proposed model we use heyperbolic secont transformation function in hiden layer of neural network part and bfgs teqnique in optimization part. In comparison with existing similar neural networks proposed model provides solutions with high accuracy. Numerica...

A New Inequality for Superdiffusions and Its Applications to Nonlinear Differential Equations

Our motivation is the following problem: to describe all positive solutions of a semilinear elliptic equation Lu = uα with α > 1 in a bounded smooth domain E ⊂ Rd. In 1998 Dynkin and Kuznetsov solved this problem for a class of solutions which they called σ-moderate. The question if all solutions belong to this class remained open. In 2002 Mselati proved that this is true for the equation ∆u = ...

A generalized Volterra–Fredholm integral inequality and its applications to fractional differential equations

*Correspondence: [email protected] 2Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia Full list of author information is available at the end of the article Abstract In this paper, we derive a new generalized Volterra–Fredholm integral inequality and use it to study the dependence of solutions on the ini...

Introduction to Ordinary Differential Equations