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Critical exponents for semilinear equations of mixed elliptic-hyperbolic and degenerate types

✍ Scribed by Daniela Lupo; Kevin R. Payne

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
222 KB
Volume
56
Category
Article
ISSN
0010-3640

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✦ Synopsis

Abstract

For semilinear Gellerstedt equations with Tricomi, Goursat or Dirichlet boundary conditions we prove Pohozaev type identities and derive non existence results that exploit an invariance of the linear part with respect to certain nonhomogeneous dilations. A critical exponent phenomenon of power type in the nonlinearity is exhibited in these mixed elliptic hyperbolic or degenerate settings where the power is one less than the critical exponent in a relevant Sobolev imbedding. © 2002 Wiley Periodicals, Inc.

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