Multiple Solutions for Nonlinear Elliptic Equations on Compact Riemannian Manifolds
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چکیده
Let (M, g) be a smooth, compact Riemannian n-manifold, and h be a Hölder continuous function on M . We prove the existence of multiple changing sign solutions for equations like ∆gu + hu = |u| ∗−2 u, where ∆g is the Laplace–Beltrami operator and the exponent 2∗ = 2n/ (n− 2) is critical from the Sobolev viewpoint.
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