A Second-Order Boundary Value Problem with Nonlinear and Mixed Boundary Conditions : Existence, Uniqueness, and Approximation

الملخص EN

A second-order boundary value problem with nonlinear and mixed two-point boundary conditions is considered, Lx=f(t,x,x′), t∈(a,b), g(x(a),x(b),x′(a),x′(b))=0, x(b)=x(a) in which L is a formally self-adjoint second-order differential operator.

Under appropriate assumptions on L, f, and g, existence and uniqueness of solutions is established by the method of upper and lower solutions and Leray-Schauder degree theory.

The general quasilinearization method is then applied to this problem.

Two monotone sequences converging quadratically to the unique solution are constructed.