2020/02/25 by Biagi, Stefano, Calamai, Alessandro, Marcelli, Cristina +1 · 1 citation
#34B16 #34K10 #34L30 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics
paper · doi:10.48550/arxiv.2002.10862
We study boundary value problems associated with singular, strongly nonlinear differential equations with functional terms of type (Φ(k(t) x'(t)))' + f(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-Laplacian operator, of a nonnegative 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.