Existence of solutions and monotone iterative method for infinite systems of parabolic differential-functional equations

Stanisław Brzychczy

Displaying similar documents to “Existence of solutions and monotone iterative method for infinite systems of parabolic differential-functional equations”

On the existence of solutions of nonlinear infinite systems of parabolic differential-functional equations.

Brzychczy, Stanisław (2002)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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Existence and uniqueness of solutions Cauchy problem for nonlinear infinite systems of parabolic differential-functional equations.

Pudełko, Anna (2002)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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Quasilinearization methods for nonlinear parabolic equations with functional dependence.

Bychowska, A. (2002)

Georgian Mathematical Journal

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Existence of solutions of the Cauchy problem for semilinear infinite systems of parabolic differential-functional equations.

Pudełko, Anna (2004)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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Initial-boundary value problems for impulsive parabolic functional differential equations

D. Bainov, Zdzisław Kamont, E. Minchev (1996)

Applicationes Mathematicae

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Theorems on differential inequalities generated by an initial-boundary value problem for impulsive parabolic functional differential equations are considered. Comparison results implying uniqueness criteria are proved.

Quasi-linearisation methods for a nonlinear heat equation with functional dependence.

Leszczyński, Henryk (2000)

Georgian Mathematical Journal

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$L_{\infty}$ -estimates for solutions of nonlinear parabolic systems with gradient linear growth

Wojciech Zajączkowski (1996)

Banach Center Publications

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Existence of weak solutions and an $L_{\infty}$ -estimate are shown for nonlinear nondegenerate parabolic systems with linear growth conditions with respect to the gradient. The $L_{\infty}$ -estimate is proved for equations with coefficients continuous with respect to x and t in the general main part, and for diagonal systems with coefficients satisfying the Carathéodory condition.

Higher integrability for weak solutions of higher order degenerate parabolic systems.

Bögelein, Verena (2008)

Annales Academiae Scientiarum Fennicae. Mathematica

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Infinite systems of hyperbolic differential-functional inequalities.

Jaruszewska-Walczak, Danuta (2005)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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Ordinary differential equations with nonlinear boundary conditions.

Jankowski, Tadeusz (2002)

Georgian Mathematical Journal

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First order partial functional differential equations with unbounded delay.

Kamont, Z., Kozieł, S. (2003)

Georgian Mathematical Journal

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$L_{\infty}$ -estimate for solutions of nonlinear parabolic systems

Wojciech Zajączkowski (1996)

Banach Center Publications

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We prove existence of weak solutions to nonlinear parabolic systems with p-Laplacians terms in the principal part. Next, in the case of diagonal systems an $L_{\infty}$ -estimate for weak solutions is shown under additional restrictive growth conditions. Finally, $L_{\infty}$ -estimates for weakly nondiagonal systems (where nondiagonal elements are absorbed by diagonal ones) are proved. The $L_{\infty}$ -estimates are obtained by the Di Benedetto methods.

Monotone method for nonlinear second order periodic boundary value problems with Carathéodory functions

Ming-Xing Wang, Alberto Cabada, Juan J. Nieto (1993)

Annales Polonici Mathematici

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The purpose of this paper is to study the periodic boundary value problem -u''(t) = f(t,u(t),u'(t)), u(0) = u(2π), u'(0) = u'(2π) when f satisfies the Carathéodory conditions. We show that a generalized upper and lower solution method is still valid, and develop a monotone iterative technique for finding minimal and maximal solutions.

On the Chaplyghin method for generalized solutions of partial differential functional equations.

Czernous, Wojciech (2005)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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