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Featured researches published by Smita Pati.


Archive | 2014

Theory of third-order differential equations

Seshadev Padhi; Smita Pati

Preface.- Chapter 1: Introduction.- Chapter 2: Behaviour of Solutions of Linear Homogeneous Differential Equations of Third Order.- Chapter 3: Oscillation of Solutions of Linear Nonhomogeneous Differential Equations of Third Order.- Chapter 4: Oscillation and Nonoscillation of Homogeneous Third-order Nonlinear Differential Equations.- Chapter 5: Oscillation and Nonoscillation of Nonlinear Nonhomogeneous Differential Equations of Third Order.- Chapter 6: Oscillatory and Asymptotic Behavior of Solutions of Third Order Delay Differential Equations.- Chapter 7: Stability of Third Order Differential Equations.- References.


Journal of Difference Equations and Applications | 2010

Multiple positive periodic solutions for a nonlinear first order functional difference equation

Julio G. Dix; Seshadev Padhi; Smita Pati

We obtain sufficient conditions for the existence of at least three non-negative periodic solutions for the first order functional difference equation Our main tool is the Leggett–Williams fixed point theorem, and our main application is a hematopoiesis model in population dynamics.


Applicable Analysis | 2009

Multiple periodic solutions for system of first-order differential equation

Seshadev Padhi; Smita Pati

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.


International Journal of Dynamical Systems and Differential Equations | 2009

Multiple positive periodic solutions for nonlinear first order functional difference equations

Seshadev Padhi; Smita Pati; Shilpee Srivastava

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.


Fractional Calculus and Applied Analysis | 2018

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

Seshadev Padhi; John R. Graef; Smita Pati

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,


Turkish Journal of Mathematics | 2017

Positive solutions of first order boundary value problems with nonlinear nonlocal boundary conditions

Smita Pati; Seshadev Padhi


Archive | 2014

Oscillation and Nonoscillation of Nonlinear Nonhomogeneous Differential Equations of Third Order

Seshadev Padhi; Smita Pati

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


Archive | 2014

Behaviour of Solutions of Linear Homogeneous Differential Equations of Third Order

Seshadev Padhi; Smita Pati


Archive | 2014

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

Seshadev Padhi; Smita Pati

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


Archive | 2014

Oscillation and Nonoscillation of Homogeneous Third-Order Nonlinear Differential Equations

Seshadev Padhi; Smita Pati

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Seshadev Padhi

Birla Institute of Technology

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John R. Graef

University of Tennessee at Chattanooga

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Shilpee Srivastava

Birla Institute of Technology

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