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Bound states for semilinear Schrödinger equations with sign-changing potential

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We study the existence and the number of decaying solutions for the semilinear Schrödinger equations \({-\varepsilon^{2}\Delta u + V(x)u = g(x,u)}\), \({\varepsilon > 0}\) 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 \({|u| \to \infty}\) .

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Correspondence to Andrzej Szulkin.

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Ding, Y., Szulkin, A. Bound states for semilinear Schrödinger equations with sign-changing potential. Calc. Var. 29, 397–419 (2007).

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