Advances in Differential Equations

Concentration of solutions of a semilinear PDE with slow spatial dependence

Robert Magnus

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The problem $-\epsilon^2\nabla\cdot(P( x)\nabla u)+F(V( x),u)=0$ is studied in the whole of ${\mathbb R}^n$, where $V(x)$ is a multidimensional potential and $P(x)$ a matrix function. Under general conditions solutions are constructed for small positive $\epsilon$ having simple concentration properties. The asymptotic form of the solution is studied as $\epsilon\to 0$ as well as its positivity.

Article information

Adv. Differential Equations, Volume 14, Number 3/4 (2009), 341-374.

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J60: Nonlinear elliptic equations


Magnus, Robert. Concentration of solutions of a semilinear PDE with slow spatial dependence. Adv. Differential Equations 14 (2009), no. 3/4, 341--374.

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