Seshadev Padhi

Multiple periodic solutions for a nonlinear first order functional differential equations with applications to population dynamics

Abstract In this work using Legget–Williams multiple fixed point theorem, we have obtained different sufficient conditions for the existence of at least three nonnegative periodic solutions for the first order functional differential equations of the form y ′ ( t ) = - a ( t ) y ( t ) + λ f ( t , y ( h ( t ) ) ) , using Legget–Williams multiple fixed point theorem.

Existence of three periodic solutions for a nonlinear first order functional differential equation

Abstract In this paper, we use Leggett–Williams multiple fixed point theorem to obtain different sufficient conditions for the existence of at least three nonnegative periodic solutions of the first order functional differential equation of the form y ′ ( t ) = - a ( t ) y ( t ) + λ f ( t , y ( h ( t ) ) ) . Some applications to mathematical ecological models are given.

Existence of multiple positive periodic solutions for delay differential equation whose order is a multiple of 4

Abstract This article shows the existence of positive periodic solutions for retarded, advanced, neutral, and ordinary differential equations whose order is a multiple of 4. First, we find a positive Green’s function explicitly. Then assuming that the coefficient of the unknown in the linear part of the equation is bounded above and below by positive constants, we find one and then three solutions by applying the Krasnoselskii and Legget–William fixed point theorems.

Multiple periodic solutions for system of first-order differential equation

Sufficient conditions have been obtained for the existence of at least two non-negative periodic solutions to a system of first-order nonlinear functional differential equations. Applications to some ecological models are given.

Multiple positive periodic solutions for nonlinear first order functional difference equations

Sufficient conditions have been obtained for the existence of at least three positive T-periodic solutions for the first order functional difference equations of the forms Δx(n) = −a(n)x(n) + λb(n)f(n, x(h(n))) and Δx(n) = a(n)x(n) − λb(n)f(n, x(h(n))). Leggett-Williams multiple fixed point theorem have been used to prove our results. We have applied our results to some mathematical models in population dynamics and obtained some interesting results. The results are new in the literature.

Multiple positive solutions for a boundary value problem with nonlinear nonlocal Riemann-Stieltjes integral boundary conditions

Abstract In this paper, we study the existence of positive solutions to the fractional boundary value problem D0+αx(t)+q(t)f(t,x(t))=0,0<t<1,

Oscillation and Nonoscillation of Nonlinear Nonhomogeneous Differential Equations of Third Order

\begin{array}{} \displaystyle D^{\alpha }_{0+}x(t)+q(t)f(t,x(t))=0, \,\, 0\lt t \lt1, \end{array}

Oscillatory and Asymptotic Behaviour of Solutions of Third-Order Delay Differential Equations

together with the boundary conditions x(0)=x′(0)=⋯=x(n−2)(0)=0,D0+βx(1)=∫01h(s,x(s))dA(s),