Abstract
We consider the differential equation ℓ ( u ) = F ( u ) , where ℓ is a formally self-adjoint second-order differential expression and F is nonlinear, with nonlinear boundary conditions. Under appropriate assumptions on ℓ , F and the boundary conditions, existence of solutions is established using the method of lower and upper solutions. A generalized quasilinearization method is then developed for this problem and we obtain two monotonic sequences of approximate solutions converging quadratically to a solution of the equation.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
