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- Title
Boundary value problems associated with singular strongly nonlinear equations with functional terms.
- Authors
Biagi, Stefano; Calamai, Alessandro; Marcelli, Cristina; Papalini, Francesca
- Abstract
We study boundary value problems associated with singular, strongly nonlinear differential equations with functional terms of type (Φ(k(t) x′ (t)))′ + ƒ(t, Gx(t))ρ(t, x′(t)) = 0, on a compact interval [a, b]. These equations are quite general due to the presence of a strictly increasing homeomorphism Φ, the so-called Φ-Laplace operator, of a non-negative function k, which may vanish on a set of null measure, and moreover of a functional term Gx. We look for solutions, in a suitable weak sense, which belong to the Sobolev space W1,1([a, b]). Under the assumptions of the existence of a well-ordered pair of upper and lower solutions and of a suitable Nagumo-type growth condition, we prove an existence result by means of fixed point arguments.
- Subjects
FUNCTIONAL equations; BOUNDARY value problems; NONLINEAR equations; FUNCTIONAL differential equations; NONLINEAR differential equations
- Publication
Advances in Nonlinear Analysis, 2021, Vol 10, Issue 1, p684
- ISSN
2191-9496
- Publication type
Article
- DOI
10.1515/anona-2020-0131