We look for positive solutions to the nonlinear Schrödinger equation -ε2Δu - V(x)f′ (u) = 0 in ℝN, where V is a continuous bounded positive potential and f satisfies particular growth conditions which make our problem fall in the so called "zero mass case". We prove an existence result for any ε > 0, and a multiplicity result for ε sufficiently small.
On a "zero mass" nonlinear Schrödinger equation / Azzollini, A.; Pomponio, Alessio. - In: ADVANCED NONLINEAR STUDIES. - ISSN 1536-1365. - 7:4(2007), pp. 599-627. [10.1515/ans-2007-0406]
On a "zero mass" nonlinear Schrödinger equation
POMPONIO, Alessio
2007-01-01
Abstract
We look for positive solutions to the nonlinear Schrödinger equation -ε2Δu - V(x)f′ (u) = 0 in ℝN, where V is a continuous bounded positive potential and f satisfies particular growth conditions which make our problem fall in the so called "zero mass case". We prove an existence result for any ε > 0, and a multiplicity result for ε sufficiently small.File in questo prodotto:
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