Zero in the Spectrum

Martin Schechter

Chapter Chapter 8 in Critical Point Theory, 2020, pp 113-130 from Springer

Abstract: Abstract In the previous chapter we noted that in our study of semilinear elliptic partial differential equations of the form A u = f ( x , u ) , u ∈ D $$\displaystyle \mathcal A u = f(x,u), u \in D $$ in unbounded domains, we required that the resolvent set of A $$\mathcal A$$ not be empty. For convenience, we assumed that it contain 0. This allowed us to choose an interval ( a , b ) ⊂ ρ ( A ) , $$(a,b) \subset \rho (\mathcal A),$$ where a

Date: 2020
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DOI: 10.1007/978-3-030-45603-0_8

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