Abstract
Many elliptic semilinear problems can be described in the following way. Let Ω be a domain in Rn and let A be a selfadjoint operator on L2(Ω). We assume that A ≥ λ0 > 0 and that
for some m > 0, where C ∞0 (Ω) denotes the set of test functions in Ω (i.e., infinitely differentiable functions with compact supports in Ω) and Hm,2(Ω) denotes the Sobolev space described in Appendix I to this chapter. If m is an integer, the norm in Hm,2(Ω) is given by
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© 1999 Springer Science+Business Media New York
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Schechter, M. (1999). Semilinear Boundary Value Problems. In: Linking Methods in Critical Point Theory. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1596-7_3
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DOI: https://doi.org/10.1007/978-1-4612-1596-7_3
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7210-6
Online ISBN: 978-1-4612-1596-7
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