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Periodic problems and problems with discontinuities for nonlinear parabolic equations

Tiziana Cardinali, Nikolaos S. Papageorgiou (2000)

Czechoslovak Mathematical Journal

In this paper we study nonlinear parabolic equations using the method of upper and lower solutions. Using truncation and penalization techniques and results from the theory of operators of monotone type, we prove the existence of a periodic solution between an upper and a lower solution. Then with some monotonicity conditions we prove the existence of extremal solutions in the order interval defined by an upper and a lower solution. Finally we consider problems with discontinuities and we show that...

Periodic solutions for nonlinear elliptic equations. Application to charged particle beam focusing systems

Mihai Bostan, Eric Sonnendrücker (2006)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We study the existence of spatial periodic solutions for nonlinear elliptic equations - Δ u + g ( x , u ( x ) ) = 0 , x ∈ ℝ N where g is a continuous function, nondecreasing w.r.t. u . We give necessary and sufficient conditions for the existence of periodic solutions. Some cases with nonincreasing functions g are investigated as well. As an application we analyze the mathematical model of electron beam focusing system and we prove the existence of positive periodic solutions for the envelope equation. We present also numerical simulations....

Periodic solutions for nonlinear elliptic equations. Application to charged particle beam focusing systems

Mihai Bostan, Eric Sonnendrücker (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

We study the existence of spatial periodic solutions for nonlinear elliptic equations - Δ u + g ( x , u ( x ) ) = 0 , x ∈ ℝ N where g is a continuous function, nondecreasing w.r.t. u. We give necessary and sufficient conditions for the existence of periodic solutions. Some cases with nonincreasing functions g are investigated as well. As an application we analyze the mathematical model of electron beam focusing system and we prove the existence of positive periodic solutions for the envelope equation. We present also numerical simulations. ...

Periodic solutions of a nonlinear evolution problem

Nelson Nery Oliveira Castro, Nirzi G. de Andrade (2002)

Applications of Mathematics

In this paper we prove existence of periodic solutions to a nonlinear evolution system of second order partial differential equations involving the pseudo-Laplacian operator. To show the existence of periodic solutions we use Faedo-Galerkin method with a Schauder fixed point argument.

Periodic solutions of a three-species periodic reaction-diffusion system

Tiantian Qiao, Jiebao Sun, Boying Wu (2011)

Annales Polonici Mathematici

We study a periodic reaction-diffusion system of a competitive model with Dirichlet boundary conditions. By the method of upper and lower solutions and an argument similar to that of Ahmad and Lazer, we establish the existence of periodic solutions and also investigate the stability and global attractivity of positive periodic solutions under certain conditions.

Periodic solutions of degenerate differential equations in vector-valued function spaces

Carlos Lizama, Rodrigo Ponce (2011)

Studia Mathematica

Let A and M be closed linear operators defined on a complex Banach space X. Using operator-valued Fourier multiplier theorems, we obtain necessary and sufficient conditions for the existence and uniqueness of periodic solutions to the equation d/dt(Mu(t)) = Au(t) + f(t), in terms of either boundedness or R-boundedness of the modified resolvent operator determined by the equation. Our results are obtained in the scales of periodic Besov and periodic Lebesgue vector-valued spaces.

Currently displaying 161 – 180 of 279