Core Functions

Martin Schechter

Chapter Chapter 11 in Critical Point Theory, 2020, pp 191-211 from Springer

Abstract: Abstract Let A $$\mathcal A$$ be a self-adjoint operator on L 2( Ω), where Ω is a bounded domain in ℝ n . $$\mathbb R^n.$$ Let f(x, t) be a Carathéodory function on Ω × ℝ . $$ \Omega \times \mathbb R.$$ A well-known semilinear problem is to solve A u = f ( x , u ) , u ∈ D ( A ) . $$\displaystyle \mathcal A u = f(x,u), \quad u \in D(\mathcal A). $$ In particular, one searches for properties of f(x, t) which guarantee the existence of solutions. This is not a trivial situation; there does not appear to be a criterion which tells us whether or not the problem is solvable.

Date: 2020
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-45603-0_11

Ordering information: This item can be ordered from
http://www.springer.com/9783030456030

DOI: 10.1007/978-3-030-45603-0_11

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().