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Zbl 1157.58006
Hirano, Norimichi
Multiple existence of solutions for a nonlinear elliptic problem on a Riemannian manifold. (English)
[J] Nonlinear Anal., Theory Methods Appl. 70, No. 2, A, 671-692 (2009). ISSN 0362-546X

Let $(M,g)$ be a compact, connected and orientable smooth $N$-dimensional Riemannian manifold without boundary, and let $p\in(2,2^*)$ with $2^*=2N/(N-2).$ The author derives the rexistence of multiple solutions to the problem $$ -\varepsilon^2\Delta_gu+u=\vert u\vert ^{p-2}u\quad \text{on}\ M $$ with $\Delta_g$ standing for the Laplacian operator over $M.$
[Dian K. Palagachev (Bari)]

MSC 2000:: *58J05 Elliptic equations on manifolds, general theory
35J65 (Nonlinear) BVP for (non)linear elliptic equations

Keywords: multiplicity; nonlinear elliptic problem; Riemannian manifold

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