Results 41 to 50 of about 57,536 (162)
A singular functional‐differential equation [PDF]
International Journal of Mathematics and Mathematical Sciences, 1982 The representation of the Hardy‐Lebesque space by means of the shift operator is used to prove an existence theorem for a singular functional‐differential equation which yields, as a corollary, the well known theory of Frobenius for second order differential equations.
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Impulsive functional-differential equations with nonlocal conditions
International Journal of Mathematics and Mathematical Sciences, 2002 The existence, uniqueness, and continuous dependence of a mild solution of an impulsive functional-differential evolution nonlocal Cauchy problem in general Banach spaces are studied.
Haydar Akça +2 more
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Oscillation of certain functional differential equations [PDF]
Computers & Mathematics with Applications, 1994 The author presents several sufficient conditions for all bounded solutions to the linear system of delay differential equations \[ (-1)^{m+1}\frac {d^m y_i(t)}{d t^m}+\sum _{j=1}^{n}q_{ij}y_i(t-h_{ij})=0, \quad m\geq 1,\;i=1,2,\dots,n, \] to be oscillatory.
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Oscillation criteria for functional differential equations
Electronic Journal of Differential Equations, 2005 Consider the first-order linear delay differential equation $$ x'(t)+p(t)x(au (t))=0,quad tgeq t_{0}, $$ and the second-order linear delay equation $$ x''(t)+p(t)x(au (t))=0,quad tgeq t_{0}, $$ where $p$ and $au $ are continuous functions on $[t_{0 ...
Ioannis P. Stavroulakis
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Stability theory for functional-differential equations [PDF]
Transactions of the American Mathematical Society, 1979 We consider a system of functional differential equations x ′ ( t ) = F ( t , x ( ⋅ ) ) x’\,(t)\, = \,\mathcal {F}\,(t,\,x( \cdot )) , together with a Liapunov functional
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Multiple solutions of nonlinear partial functional differential equations and systems
Electronic Journal of Qualitative Theory of Differential Equations, 2019 We shall consider weak solutions of initial-boundary value problems for semilinear and nonlinear parabolic differential equations with certain nonlocal terms, further, systems of elliptic functional differential equations.
László Simon
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Electronic Journal of Qualitative Theory of Differential Equations, 2016 The periodic boundary value problem for second order linear functional differential equations with pointwise restrictions (instead of integral ones) is considered. Sharp sufficient conditions for the solvability are obtained.
Eugene Bravyi
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A Partial Functional Differential Equation
Journal of Mathematical Analysis and Applications, 2001 The author of this interesting paper investigates the partial functional differential equation \[ \partial u(x,t)\partial t =k \partial^2 u(x,t)\partial x^2+ru(x,t-T)[1-u(x,t)], \;\;t\geq 0, \;\;x\in [{}0,\pi ]{} \] under the boundary condition \(u(0,t)=u(\pi ,t)=0\) (\(t>0\)) and \(u(x,s)=\phi (x,s)\), \(-T\leq s\leq 0\), \(0\leq x\leq \pi \).
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Distributional and entire solutions of ordinary differential and functional differential equations
International Journal of Mathematics and Mathematical Sciences, 1983 A brief survey of recent results on distributional and entire solutions of ordinary differential equations (ODE) and functional differential equations (FDE) is given. Emphasis is made on linear equations with polynomial coefficients.
S. M. Shah, Joseph Wiener
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On Nonautonomous Functional Differential Equations
Journal of Mathematical Analysis and Applications, 1999 The author investigates the existence of an evolution family for the nonautonomous Cauchy problem \[ x'(t)= A(t) x(t),\quad 0\leq s\leq t\leq T,\quad x(s)= x, \] in a Banach space \(X\). Each \(A(t)\) is a linear operator on \(X\). The following result is obtained: Let \(X\), \(Y\), and \(D\) be Banach spaces, \(D\) densely and continuously imbedded in
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