Wolfram Mathematica application to determination of the number of solutions for certain nonlinear boundary value problems

Abstract

The nonlinear boundary value problem (BVP) x 00 ¼ À ax þ qðtÞ x φðxÞ, where φðxÞ ¼ x or φðxÞ ¼ x 2 , x 0 ðÀ 1Þ ¼ x 0 ð1Þ ¼ 0 with step-wise function qðtÞ, is studied. The number of nontrivial solutions for the problem is estimated. For the case, where qðtÞ ¼ b ¼ const > 0, the exact number of solutions for the boundary value problem is given. With the help of Wolfram Mathematica, the examples show several ways to determine the number of solutions for BVP.