The Two-dimensional Lazer-mckenna Conjecture for an Exponential Nonlinearity
نویسنده
چکیده
where Ω is a bounded, smooth domain in R, φ1 is a positive first eigenfunction of the Laplacian under Dirichlet boundary conditions and h ∈ C(Ω̄). We prove that given k ≥ 1 this problem has at least k solutions for all sufficiently large s > 0, which answers affirmatively a conjecture by Lazer and McKenna [22] for this case. The solutions found exhibit multiple concentration behavior around maxima of φ1 as s → +∞.
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