We consider the equation -u" = g(u), u(x) ∈ H1(R). (0.1) Under general assumptions on the nonlinearity g we prove that the, unique up to translation, solution of (0.1) is at the mountain pass level of the associated functional. This result extends a corresponding result for least energy solutions when (0.1) is set on RN.
- Least energy solution
- Mountain pass characterization
ASJC Scopus subject areas
- Statistical and Nonlinear Physics