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arXiv · 1012.5672

Positive solutions for singularly perturbed nonlinear elliptic problem on manifolds via Morse theory

Marco G. Ghimenti·Anna Maria Micheletti
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Abstract

Given (M, g0) we consider the problem -ε^2Delta_{g0+h}u + u = (u+)^{p-1} with (ε, h) \in (0, ε0) \times Bρ. Here Bρ is a ball centered at 0 with radius ρ in the Banach space of all Ck symmetric covariant 2-tensors on M. Using the Poincaré polynomial of M, we give an estimate on the number of nonconstant solutions with low energy for (ε, h) belonging to a residual subset of (0, ε0) \times Bρ, for (ε0, ρ) small enough.

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Marco G. Ghimenti, Anna Maria Micheletti. 2010-12-27. Positive solutions for singularly perturbed nonlinear elliptic problem on manifolds via Morse theory. https://arxiv.org/abs/1012.5672

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