Nonlinear eigenvalues and mountain pass methods (Q1310469)

The authors give a detailed account of mountain pass lemmas for \(C^ 1\) functionals \(G\) on a Hilbert space, where the admissible paths are restricted to fixed regions. A typical example for such a region is the set \(\{u\): \(u\in H\), \(F(u)\leq R\}\), where \(F\) is another \(C^ 1\) functional and \(R>0\). The imposed convergence conditions are essentially weaker than the classical Galois-Smale condition.