Sublinear eigenvalue problems on compact Riemannian manifolds with applications in Emden-Fowler equations

被引:13
作者
Kristaly, Alexandru [1 ]
Radulescu, Vicentiu [2 ,3 ]
机构
[1] Univ Babes Bolyai, Dept Econ, Cluj Napoca 400591, Romania
[2] Univ Craiova, Dept Math, Craiova 200585, Romania
[3] Acad Romana, Inst Math Simion Stoilow, Bucharest 014700, Romania
关键词
Emden-Fowler equation; sublinear eigenvalue problem; multiple solutions; NONLINEAR ELLIPTIC-EQUATIONS; THEOREM;
D O I
10.4064/sm191-3-5
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let (M, g) be a compact Riemannian manifold without boundary, with dim M >= 3, and f : R -> R a continuous function which is sublinear at infinity. By various variational approaches, existence of multiple solutions of the eigenvalue problem -Delta(g)w + alpha(sigma)w = (K) over tilde(lambda, sigma)f(w), sigma is an element of M, w is an element of H(1)(2)(M), is established for certain eigenvalues lambda > 0, depending on further properties of f and on explicit forms of the function (K) over tilde. Here, Delta(g) stands for the Laplace-Beltrami operator on (M, g), and alpha, (K) over tilde are smooth positive functions. These multiplicity results are then applied to solve Emden-Fowler equations which involve sublinear terms at infinity.
引用
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页码:237 / 246
页数:10
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