Sublinear eigenvalue problems on compact Riemannian manifolds with applications in Emden–Fowler equations
Tom 191 / 2009
Streszczenie
Let be a compact Riemannian manifold without boundary, with \dim M\geq 3, and f:\mathbb R \to \mathbb R a continuous function which is {sublinear} at infinity. By various variational approaches, existence of multiple solutions of the eigenvalue problem -{\mit\Delta}_{g} \omega+\alpha (\sigma) \omega= \tilde K(\lambda,\sigma)f(\omega),\ \quad \sigma\in M,\, \omega\in H_1^2(M), is established for certain eigenvalues \lambda>0, depending on further properties of f and on explicit forms of the function \tilde K. Here, {\mit\Delta}_{g} stands for the Laplace–Beltrami operator on (M,g), and \alpha, \tilde K are smooth positive functions. These multiplicity results are then applied to solve Emden–Fowler equations which involve sublinear terms at infinity.
