Superlinear Problems

Abstract

This chapter deals with superlinear problems, i.e., nonlinear Dirichlet boundary value problems whose nonlinearity f(u) is superlinear at ∞, namely

$$\mathop {\lim }\limits_{u \to + \infty } \frac{{f(u)}}{u} = + \infty $$

In this case an appropriate approach seems to be critical point theory. Actually, the mountain pass theorem or the linking theorem can be used to find solutions. We also show how to study superlinear problems by using the topological degree.