We study boundary value problems associated with singular, strongly nonlinear differential equations with functional terms of type (φ (k (t) x ′ (t))) ′ + f (t, G x (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.

Boundary value problems associated with singular strongly nonlinear equations with functional terms

Biagi S.;
2020-01-01

Abstract

We study boundary value problems associated with singular, strongly nonlinear differential equations with functional terms of type (φ (k (t) x ′ (t))) ′ + f (t, G x (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.
2020
boundary-value problems
functional ODEs
singular ODEs
upper/lower solutions
φ-Laplace operator
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1183025
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