ON SPIKES ON LINES FOR A NEUMANN SUPERLINEAR AMBROSETTI-PRODI TYPE PROBLEM

. Given a smooth bounded domain Ω ⊂ R n and consider the problem ∂ Ω where p is subcritical exponent ( p > 1 if n = 2 and 1 < p < n +2 n − 2 if n ≥ 3), σ > 0 is a large parameter and ν denotes the outward normal of ∂ Ω. Let Γ be an interior straighline intersecting orthogonally with ∂ Ω. Assuming moreover that Γ satisfies a non-degeneracy condition, we construct a new class of solutions which consist of large number of spikes concentrating on Γ, showing as in [5, 6] that higher dimensional concentration can exist without

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