Affiliation:
1. Dipartimento di Matematica, Politecnico di Milano , Via Bonardi 9 , Milano , Italy
2. Dipartimento di Ingegneria Civile, Edile e Architettura, Università Politecnica delle Marche , Via Brecce Bianche 12 , Ancona , Italy
3. Dipartimento di Ingegneria Industriale e Scienze Matematiche, Università Politecnica delle Marche , Via Brecce Bianche 12 , Ancona , Italy
Abstract
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
,
$$\big({\it \Phi}(k(t)\,x'(t))\big)' + f(t,{{\mathcal{G}}}_x(t))\,\rho(t, x'(t)) = 0,$$
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 G
x
. We look for solutions, in a suitable weak sense, which belong to the Sobolev space W
1,1([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.
Cited by
6 articles.
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