Fractional Schrödinger equations involving potential vanishing at infinity and supercritical exponents

This work studies the existence of positive solutions for fractional Schrödinger equations of the form ( - Δ ) s u + V ( x ) u = g ( u ) + λ | u | q - 2 u in R N , where s ∈ ( 0 , 1 ) , N > 2 s , V : R N → R is a potential function which can vanish at infinity, g : R → R is superlinear and has su...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2020-08, Vol.71 (4), Article 129
Main Authors: Cardoso, J. A., Prazeres, D. S. dos, Severo, U. B.
Format: Article
Language:English
Subjects:
Engineering
Infinity
Mathematical analysis
Mathematical Methods in Physics
Schrodinger equation
Theoretical and Applied Mechanics
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Summary:This work studies the existence of positive solutions for fractional Schrödinger equations of the form ( - Δ ) s u + V ( x ) u = g ( u ) + λ | u | q - 2 u in R N , where s ∈ ( 0 , 1 ) , N > 2 s , V : R N → R is a potential function which can vanish at infinity, g : R → R is superlinear and has subcritical growth, the exponent q ≥ 2 s ∗ : = 2 N / ( N - 2 s ) and λ is a nonnegative parameter. Our approach is based on a truncation argument in combination with variational techniques and the Moser iteration method.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-020-01354-0