Existence-uniqueness and iterative methods for third-order boundary value problems
Various types of existence conditions are given for the solution of the 3-point boundary value problem \[ x\prime''=f(t,x,x',x'');\quad x'(a)=A,\quad x(b)=B,\quad x'(c)=C, \] utilizing the Schauder fixed point principle. The case when f(t,x,y,z) is linear in x,y,z is separately considered. An iterative scheme for approximating the solution is justified. Finally, illustrative examples are considered.
scientific article; zbMATH DE number 4000404
scientific article