Journal
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
Volume 29, Issue 3, Pages 397-419Publisher
SPRINGER
DOI: 10.1007/s00526-006-0071-8
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We study the existence and the number of decaying solutions for the semilinear Schrodinger equations - epsilon(2)Delta u + V( x) u = g( x, u), epsilon > 0 small, and - Delta u + lambda V(x) u = g( x, u) lambda > 0 large. The potential V may change sign and g is either asymptotically linear or superlinear ( but subcritical) in u as vertical bar u vertical bar -> infinity.
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