Schrodinger Equation With Multiparticle Potential and Critical Nonlinearity

Chabrowski, Jan;Szulkin, Andrzej;Willem, Michel
(2009) Topological Methods in Nonlinear Analysis — Vol. 34, n° 2, p. 201-211 (2009)

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  • Chabrowski, Jan
    Author
  • Szulkin, Andrzej
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  • Willem, MichelUCLouvain
    Author
Abstract
We study the existence and non-existence of ground states for the Schrodinger equations -Delta u - lambda Sigma(i<j) u/vertical bar x(i) - x(j)vertical bar(2) = vertical bar u vertical bar(2)* -(2)u, x = (x(1), ... , x(m)) is an element of R-mN, and -Delta u -lambda u/vertical bar y vertical bar(2) = vertical bar u vertical bar(2*) (-2)u, x = (y, z) is an element of R-N. In both cases we assume lambda not equal 0 and lambda < (lambda) over bar, where (lambda) over bar is the Hardy constant corresponding to the problem.
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Chabrowski, J., Szulkin, A., & Willem, M. (2009). Schrodinger Equation With Multiparticle Potential and Critical Nonlinearity. Topological Methods in Nonlinear Analysis, 34(2), 201-211. https://hdl.handle.net/2078.5/82524 (Original work published 2009)