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By Ortega R., Tarallo M.

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Ni, I. Takagi. On the shape of least-energy solutions to a semi-linear Neumann problem, Comm. Pure App. Math. XLIV (1991), 819-851. [23] W. M. Ni, I. Takagi. Locating the peaks of least-energy solutions to a semilinear Neumann problem, Duke Math. J. 70 (1993), 247-281. [24] W. M. Ni, J. Wei. On the location and profile of spike-layer solutions to singularly perturbed semilinear Dirichlet problems, Comm. Pure App. Math. 48 (1995), 731-768. [25] Y. J. Oh. Existence of semi-classical bound states of nonlinear Schr¨ odinger equation with potential on the class (V )a , Comm.

D’Aprile. Existence, multiplicity and concentration of bound states for a quasilinear elliptic field equation, Calc. Var. PDE, to appear. [3] M. Badiale, V. Benci, T. D’Aprile. Semiclassical limit for a quasilinear elliptic field equation: one-peak and multi-peak solutions, preprint n. 25 Scuola Normale Superiore, Ottobre 1999. [4] V. Benci. Quantum phenomena in a classical model, Foundations of Physics, Vol 29 (1999), 1-29. [5] V. Benci, A. Abbondandolo. Solitons and Bohmian mechanics, Proc. Nat.

36), lim sup λh ∈ h→0+ inf rN −1 Er∗ (1), r≥r1 p inf rN −1 Er∗ (1) . 72) Now consider a generic sequence hn → 0+ . 72), provided n is sufficiently large, we can assume 1 λ hn ∈ inf rN −1 Er∗ (1), p inf rN −1 Er∗ (1) . 1 we easily deduce, up to a subsequence, vhn has a sphere of local maximum points {x ∈ RN | |x| = rhn }, ∀x ∈ RN with |x| = rhn : 1/(p−2) vhn (x) > γλhn ≥γ 1 inf rN −1 Er∗ (1) 2 r≥r1 rhn → r ≥ r1 , rN −1 Er∗ (1) = inf rN −1 Er∗ (1), r≥r1 ∀δ > 0 : lim sup sup n→+∞ x∈C(rhn −δ,rhn +δ) 30 vhn (x) ≤ 1/(p−2) ≡ V0 2p 1/(p−2) ; 1/(p−2) ≤ p inf rN −1 Er∗ (1) lim sup r≥r1 sup n→+∞ x∈C(rhn −δ,rhn +δ) vhn (x) = 0.

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Almost periodic equations and conditions of Ambrosetti-Prodi type by Ortega R., Tarallo M.


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