We investigate strongly nonlinear differential equations of the type (Phi(k(t)u′(t)))′=f(t,u(t),u′(t)),a.e.on[0,T],where Phi is a strictly increasing homeomorphism and the nonnegative functionkmay vanish on a set of measure zero. By using the upper and lower solutions method,we prove existence results for the Dirichlet problem associated with the above equation, as well as for different boundary conditions involving the function k. Our existence results require a weak form of a Wintner–Nagumo growth condition.
Boundary value problems for singular second order equations / Calamai, Alessandro; Marcelli, Cristina; Papalini, Francesca. - In: FIXED POINT THEORY AND APPLICATIONS. - ISSN 1687-1820. - ELETTRONICO. - 2018:1(2018), pp. 1-22. [10.1186/s13663-018-0645-0]
Boundary value problems for singular second order equations
Calamai, Alessandro;Marcelli, Cristina;Papalini, Francesca
2018-01-01
Abstract
We investigate strongly nonlinear differential equations of the type (Phi(k(t)u′(t)))′=f(t,u(t),u′(t)),a.e.on[0,T],where Phi is a strictly increasing homeomorphism and the nonnegative functionkmay vanish on a set of measure zero. By using the upper and lower solutions method,we prove existence results for the Dirichlet problem associated with the above equation, as well as for different boundary conditions involving the function k. Our existence results require a weak form of a Wintner–Nagumo growth condition.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
