Results 131 to 140 of about 10,120 (154)
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Linear Nonautonomous Systems of Differential Equations with a Quadratic Integral
Differential Equations, 2021The author considers the linear nonautonomous system of differential equations \[\dot x=A(t)x,\quad x\in \mathbb{R}^n,\tag{1}\] admitting the quadratic integral \[F(x,t)=(B(t)x,x)/2\tag{2}\] where the bracket (,) stands for the inner product on \(\mathbb{R}^n\).
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On the existence of integrable solutions for a nonlinear quadratic integral equation
Journal of Applied Mathematics and Computing, 2013The authors establish a theorem concerning the existence of an integrable solution of nonlinear quadratic integral equation of the form \[ x(t)=u(t,x(t))+g(t,x(t))\int_{0}^{\varphi(t)}k(t,s)f(s,x(s))ds,\, t\in I=[0,1].\tag{*} \] Chandrasekhar's integral equation \[ x(t)=1+x(t)\int_{0}^{1}\frac{1}{t+s}\psi(s)x(s)ds \] is a particular case of (*).
Bellour, Azzeddine +2 more
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Nondecreasing solutions of a quadratic singular Volterra integral equation
Mathematical and Computer Modelling, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Józef Banas, Beata Rzepka
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A Class of Quadratic Integral-Differential Equations
Complex Variables, Theory and Application: An International Journal, 2002A nonlinear integro-ordinary differential equation built up by a linear ordinary differential operator of n th order with constant coefficients and a quadratic integral term is dealt with. The integral term represents the so-called autocorrelation of the unknown function. Applying the Fourier cosine transformation, the integral-differential equation is
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Periodic solutions of quadratic Weyl fractional integral equations
Communications in Nonlinear Science and Numerical Simulation, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Qian Chen +3 more
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On Erdélyi–Kober fractional Urysohn–Volterra quadratic integral equations
Applied Mathematics and Computation, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Monotonic solutions for quadratic integral equations
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, 2011Mieczysław Cichoń, Mohamed Metwali
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Analytical Study of a ϕ− Fractional Order Quadratic Functional Integral Equation
Foundations, 2022Ahmed El-Sayed +2 more
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Monotonic solutions of a quadratic integral equation of Volterra type
Computers and Mathematics With Applications, 2004Antonio Martinon, J Banas
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Positive solutions of a quadratic integral equation
Archive for Rational Mechanics and Analysis, 1967openaire +1 more source