Existence and multiplicity of solutions for certain Dirichlet problems with nonlinearity depending on the derivative. (Q1421157)

The authors deal with the existence and multiplicity of solutions for certain Dirichlet problems with nonlinearity depending on the derivative. More precisely, they restrict themselves to the case of bounded nonlinearities and consider \[ u''(t)+ u(t)+ g(u'(t))= f(t),\quad u(0)= u(\pi)= 0, \] where \(f\in C[0,\pi]\) and \(g\in C(\mathbb{R},\mathbb{R})\) with \(g(\pm\infty)= \lim_{\xi\to\pm\infty} g(\xi)\) finite. Using Lyapunov-Schmidt reduction and certain asymptotical methods, the authors prove existence and multiplicity of solutions.