On the global set of solutions of a nonlinear ODE: theoretical and numerical description (Q1078738)

Nonlinear differential equations of the type \(-u''=f(u)+\lambda g(x)\) in (0,1), \(u(0)=u(1)=0\) are studied. Here f is a convex, nondecreasing function with \(f(0)=0\), \(f'(0)=0\), \(\lim_{s\to \pm \infty}f(s)/s=\infty\) and g is a positive function in (0,1). In the particular case, \(f(u)=u| u|^{p-1}\) and g(x)\(\equiv 1\), a complete global description of the set of solutions is given exhibiting an infinite number of bifurcation points and turning points. Some of the results regarding the positive solutions are shown to extend for a similar semilinear elliptic problem in higher dimensions.