ISSN:
1432-0606
Keywords:
Key words. Maximal monotone operator, Coercive operator, Leray—Schauder principle, Integration by parts, Compact embedding, Extremal solution, Continuous selection, Weak norm, Strong relaxation. AMS Classification. 34A60, 34B15.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract. In this paper we consider a general nonlinear boundary value problem for second-order differential inclusions. We prove two existence theorems, one for the ``convex'' problem and the other for the ``nonconvex'' problem. Then we show that the solution set of the latter is dense in the C 1 (T,R N ) -norm to the solution set of the former (relaxation theorem). Subsequently for a Dirichlet boundary value problem we prove the existence of extremal solutions and we show that they are dense in the solutions of the convexified problem for the C 1 (T,R N ) -norm . Our tools come from multivalued analysis and the theory of monotone operators and our proofs are based on the Leray—Schauder principle.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002459900106
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