We consider a strongly nonlinear differential equation of the following general type: (Φ(a(t,x(t))x′(t)))′=f(t,x(t),x′(t)),a.e. on[0,T],where f is a Carathédory function, Φ is a strictly increasing homeomorphism (the Φ -Laplacian operator), and the function a is continuous and non-negative. We assume that a(t, x) is bounded from below by a non-negative function h(t), independent of x and such that 1 / h∈ Lp(0 , T) for some p> 1 , and we require a weak growth condition of Wintner–Nagumo type. Under these assumptions, we prove existence results for the Dirichlet problem associated with the above equation, as well as for different boundary conditions. Our approach combines fixed point techniques and the upper/lower solution method.

Existence results for boundary value problems associated with singular strongly nonlinear equations

Biagi S.
;
Calamai A.;Papalini F.
2020

Abstract

We consider a strongly nonlinear differential equation of the following general type: (Φ(a(t,x(t))x′(t)))′=f(t,x(t),x′(t)),a.e. on[0,T],where f is a Carathédory function, Φ is a strictly increasing homeomorphism (the Φ -Laplacian operator), and the function a is continuous and non-negative. We assume that a(t, x) is bounded from below by a non-negative function h(t), independent of x and such that 1 / h∈ Lp(0 , T) for some p> 1 , and we require a weak growth condition of Wintner–Nagumo type. Under these assumptions, we prove existence results for the Dirichlet problem associated with the above equation, as well as for different boundary conditions. Our approach combines fixed point techniques and the upper/lower solution method.
File in questo prodotto:
File Dimensione Formato  
2020-BiagiCaPa_JFPTA.pdf

solo utenti autorizzati

Licenza: NON PUBBLICO-Accesso privato/ristretto
Dimensione 576.28 kB
Formato Adobe PDF
576.28 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11566/284544
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 5
  • ???jsp.display-item.citation.isi??? 1
social impact