Boundary-value problems for singular ODEs governed by non-linear F-Laplacians


The main aim is to prove, both on bounded and unbounded intervals, the existence of solutions for boundary-value problems associated with ODEs of the form

(*) F(a(t,x)x’(t))’=f(t,x(t),x’(t))

where F is a strictly increasing homeomorphism from R to R , the function a is continuous, non-negative and can vanish a set of zero Lebesgue measure (hence, the equation can be singular), and f is a generic Carathéodory function. Equations of the form (*) naturally arise in non-Newtonian fluid theory, reaction-diffusion processes in porus media ecc. Our goal is thus to prove the existence of solutions for these equations under different types of boundary conditions (Dirichlet, Neumann, mixed, functionals and/or non-local ecc.). Due to the great generality of conditions, the techniques we use are borrowed from the Functional Analysis (fixed-point/degree theory, method of lower/upper solutions ecc.).


Prof.ssa Cristina Marcelli email:

Prof.ssa Francesca Papalini email:

Dott. Stefano Biagi email: