By using variational techniques we provide new existence results for Yamabe-type equations with subcritical perturbations set on a compact d-dimensional (d >= 3) Riemannian manifold without boundary. As a direct consequence of our main theorems, we prove the existence of at least one solution to the following Yamabe-type problem{-Delta(g)w + alpha(sigma)w = mu K(sigma)w(d+2/d-2) + lambda(w(r-1) + f(w)), sigma is an element of Mw is an element of H-alpha(2)(M), w > 0 in M,where, as usual, Delta(g) denotes the Laplace-Beltrami operator on (M, g), alpha, K : M -> R are positive (essentially) bounded functions, r is an element of (0, 1), and f : [0, +infinity) [0, +infinity) is a subcritical continuous function. Restricting ourselves to the unit sphere S-d via the stereo-graphic projection, we furthermore solve some parametrized Emden-Fowler equations in the Euclidean case.

### Existence results for some problems on Riemannian manifolds

#### Abstract

By using variational techniques we provide new existence results for Yamabe-type equations with subcritical perturbations set on a compact d-dimensional (d >= 3) Riemannian manifold without boundary. As a direct consequence of our main theorems, we prove the existence of at least one solution to the following Yamabe-type problem{-Delta(g)w + alpha(sigma)w = mu K(sigma)w(d+2/d-2) + lambda(w(r-1) + f(w)), sigma is an element of Mw is an element of H-alpha(2)(M), w > 0 in M,where, as usual, Delta(g) denotes the Laplace-Beltrami operator on (M, g), alpha, K : M -> R are positive (essentially) bounded functions, r is an element of (0, 1), and f : [0, +infinity) [0, +infinity) is a subcritical continuous function. Restricting ourselves to the unit sphere S-d via the stereo-graphic projection, we furthermore solve some parametrized Emden-Fowler equations in the Euclidean case.
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2020
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11570/3210629`
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