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Existence and multiplicity results for a nonlinear stationary Schrödinger equation. (English) Zbl 1205.35099

Summary: We revisit Kristály’s result on the existence of weak solutions of the Schrödinger equation of the form

-Δu+a(x)u=λb(x)f(u),x N ,uH 1 ( N ),

where λ is a positive parameter, a and b are positive functions, while f: is sublinear at infinity and superlinear at the origin. In particular, by using Ricceri’s recent three critical points theorem, we show that, under the same hypotheses, a much more precise conclusion can be obtained.

35J61Semilinear elliptic equations
35J20Second order elliptic equations, variational methods
35B45A priori estimates for solutions of PDE