Infinitely Many Positive Solutions for Nonlinear Equations with Non-symmetric Potentials
نویسندگان
چکیده
We consider the following nonlinear Schrödinger equation { ∆u− (1 + δV )u + f(u) = 0 in R , u > 0 in R , u ∈ H(R ) where V is a continuous potential and f(u) is a nonlinearity satisfying some decay condition and some non-degeneracy condition, respectively. Using localized energy method, we prove that there exists a δ0 such that for 0 < δ < δ0, the above problem has infinitely many positive solutions. This generalizes and gives a new proof of the results by Cerami-Passaseo-Solimini [13]. The new techniques allow us to establish the existence of infinitely many positive bound states for elliptic systems.
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تاریخ انتشار 2013