Asymptotic theory for a critical class of third-order differential equations

Asymptotic Properties of Third-Order Delay Trinomial Differential Equations

and Applied Analysis 3 2. Main Results It will be derived that properties of E are closely connected with the corresponding secondorder differential equation ( 1 r t v′ t )′ p t v t 0 Ev as the following theorem says. Theorem 2.1. Let v t be a positive solution of Ev . Then E can be written as ( v2 t r t ( 1 v t y′ t )′)′ q t v t y σ t 0. E Proof. The proof follows from the fact that 1 v t ( v2...

The variational iteration method for a class of tenth-order boundary value differential equations

Bifurcation theory for a class of second order differential equations

We consider the existence of positive solutions of the nonlinear two point boundary value problem u′′ + λf(u) = 0, u(−1) = u(1) = 0, where f(u) = u(u − a)(u− b)(u− c)(1−u), 0 < a < b < c < 1, as the parameter λ varies through positive values. Every solution u(x) is an even function, and when it exists, it is uniquely identified by α = u(0). We study how the number of solutions changes when the ...

Theory of Hybrid Fractional Differential Equations with Complex Order

We develop the theory of hybrid fractional differential equations with the complex order $thetain mathbb{C}$, $theta=m+ialpha$, $0<mleq 1$, $alphain mathbb{R}$, in Caputo sense. Using Dhage's type fixed point theorem for the product of abstract nonlinear operators in Banach algebra; one of the operators is $mathfrak{D}$- Lipschitzian and the other one is completely continuous, we prove the exis...

ON TE EXISTENCE OF PERIODIC SOLUTION FOR CERTAIN NONLINEAR THIRD ORDER DIFFERENTIAL EQUATIONS