, Volume 106, Issue 3, pp 217-241

Elliptic and parabolic semilinear problems without conditions at infinity

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Abstract

I prove that some semilinear elliptic and parabolic problems of arbitrary even order are well-posed in all of ℝN without conditions at infinity. In particular, the growth of the data at infinity need not be limited and the solution is unique without prescription of its behavior at infinity. This is partly a higher-order generalization of the results obtained by Brezis (Appl. Math. Optim. 12, (1984), 271–282) for second-order problems.

Communicated by H. Brezis