The exact number of solutions for the second order nonlinear boundary value problem

Year, pages: 2008, 439 - 454

A second order nonlinear differential equation with homogeneous Dirichlet boundary conditions is considered. An explicit expression for the root functions for an autonomous nonlinear boundary value problem is obtained using the results of the paper [SOMORA, P.: \textit{The lower bound of the number of solutions for the second order nonlinear boundary value problem via the root functions method}, Math. Slovaca \textbf{57} (2007), 141–156]. Other assumptions are supposed to prove the monotonicity of root functions and to get the exact number of solutions. The existence of infinitely many solutions of the boundary value problem with strong nonlinearity is obtained by the root function method as well.

Somora, P. 2008. The exact number of solutions for the second order nonlinear boundary value problem. In Mathematica Slovaca, vol. 58, no.4, pp. 439-454. 0139-9918.

Somora, P. (2008). The exact number of solutions for the second order nonlinear boundary value problem. Mathematica Slovaca, 58(4), 439-454. 0139-9918.