Displaying similar documents to “Multibump solutions and asymptotic expansions for mesoscopic Allen-Cahn type equations”

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

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We study the existence of spatial periodic solutions for nonlinear elliptic equations - Δ u + g ( x , u ( x ) ) = 0 , x 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...

Spatially heteroclinic solutions for a semilinear elliptic P.D.E.

Paul H. Rabinowitz (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper uses minimization methods and renormalized functionals to find spatially heteroclinic solutions for some classes of semilinear elliptic partial differential equations