Applicable Analysis and Discrete Mathematics 2012 Volume 6, Issue 2, Pages: 174-193
Full text ( 313 KB)
Nonlocal systems of BVPS with asymptotically sublinear boundary conditions
Goodrich Christopher S.
In this paper we consider a coupled system of second-order boundary value
problems with nonlocal, nonlinear boundary conditions. By imposing only a
condition of asymptotic sublinear growth on the nonlinear boundary
functions, we are able to achieve generalizations over existing works and,
in particular, we allow for the nonlocal terms to be able to be represented
as Lebesgue-Stieltjes integrals possessing signed Borel measures. Because we
only suppose the sublinearity of the nonlinear boundary functions at
positive infinity, we also remove many of the restrictive growth assumptions
found in other recent works on closely related problems. We conclude with a
numerical example to explicate the consequences of our main result.
Keywords: Coupled system of second-order boundary value problems, nonlocal boundary condition, nonlinear boundary condition, eigenvalue, positive solution