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Search: All articles in the CMB digital archive with keyword nonlinear boundary conditions

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1. CMB 2010 (vol 53 pp. 475)

Jankowski, Tadeusz
Nonlinear Multipoint Boundary Value Problems for Second Order Differential Equations
In this paper we shall discuss nonlinear multipoint boundary value problems for second order differential equations when deviating arguments depend on the unknown solution. Sufficient conditions under which such problems have extremal and quasi-solutions are given. The problem of when a unique solution exists is also investigated. To obtain existence results, a monotone iterative technique is used. Two examples are added to verify theoretical results.

Keywords:second order differential equations, deviated arguments, nonlinear boundary conditions, extremal solutions, quasi-solutions, unique solution
Categories:34A45, 34K10

2. CMB 2008 (vol 51 pp. 140)

Rossi, Julio D.
First Variations of the Best Sobolev Trace Constant with Respect to the Domain
In this paper we study the best constant of the Sobolev trace embedding $H^{1}(\Omega)\to L^{2}(\partial\Omega)$, where $\Omega$ is a bounded smooth domain in $\RR^N$. We find a formula for the first variation of the best constant with respect to the domain. As a consequence, we prove that the ball is a critical domain when we consider deformations that preserve volume.

Keywords:nonlinear boundary conditions, Sobolev trace embedding
Categories:35J65, 35B33

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