Ruppen, Hans-Jorg2016-10-182016-10-182016-10-18201610.1007/s00526-016-1025-4https://infoscience.epfl.ch/handle/20.500.14299/130406WOS:000381989700018We analyse the existence of multiple critical points for an even functional J : H -> R in the following context: the Hilbert space H can be split into an orthogonal sum H = Y circle plus Z in such a way that inf{J(u) : u is an element of Z and parallel to u parallel to = rho >= alpha > J(0) and that here exits a point b is an element of H with parallel to b parallel to > rho and with J(b) <= J(0). We develop a new variational characterization of multiple critical levels without an assumption on the dimension of Y. Our characterization is simple and natural: we can for example avoid the notion of pseudo-index and the definition of the activated levels does not substantially differs from the one used for the lowest critical level, giving us in this way a unified view of critical levels. We apply our results to a semi-linear Schrodinger equation of the form {-Delta u + V(x)u - q(x)vertical bar u vertical bar(sigma)u = lambda u, x is an element of R-N u is an element of H-1(R-N)\{0} where lambda is inside a spectral gap bounded on both sides by parts of the essential spectrum.Variational characterization of critical valuesPartial differential equationsNon-linear Schrodinger equationsNon-linear eigenvalue problemstext::journal::journal article::research article