Abstract
For elliptic equations ε2Δu − V(x) u + f(u) = 0, x ∈ R N, N ≧ 3, we develop a new variational approach to construct localized positive solutions which concentrate at an isolated component of positive local minimum points of V, as ε → 0, under conditions on f which we believe to be almost optimal.
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Byeon, J., Jeanjean, L. Standing Waves for Nonlinear Schrödinger Equations with a General Nonlinearity. Arch Rational Mech Anal 185, 185–200 (2007). https://doi.org/10.1007/s00205-006-0019-3
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DOI: https://doi.org/10.1007/s00205-006-0019-3