Combining fixed point theorems with the method of lower and upper solutions, we get the existence of solutions to the following
nonlinear differential inclusion:
(D(x(t))F(x¢(t)))¢ Î G(t,x(t),x¢(t)) a.e. t Î I=[0,T], (D(x(t))\Phi(x'(t)))' \in G(t,x(t),x'(t)) \ \ \mbox{a.e. } t\in I=[0,T],
satisfying various nonlinear boundary conditions, covering Dirichlet, Neumann and periodic problems. Here
... [Show full abstract] Φ is a non-surjective
homeomorphism and D is a generic positive continuous function.
KeywordsDifferential inclusions–Φ-Laplacian–Nonlinear boundary conditions–Lower and upper solutions–Fixed point techniques–Nonlinear differential operators