Nonlinear elliptic problems on Riemannian manifolds and applications to Emden-Fowler type equations

被引:12
作者
Bonanno, Gabriele [1 ]
Bisci, Giovanni Molica [2 ]
Radulescu, Vicentiu D. [3 ,4 ]
机构
[1] Univ Messina, Math Sect, Dept Sci Engn & Architecture, Fac Engn, I-98166 Messina, Italy
[2] Univ Reggio Calabria, Dipartimento MECMAT, I-89124 Reggio Di Calabria, Italy
[3] Romanian Acad, Inst Math Simion Stoilow, Bucharest 014700, Romania
[4] Univ Craiova, Dept Math, Craiova 200585, Romania
关键词
SEQUENCES;
D O I
10.1007/s00229-012-0596-4
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The existence of one non-trivial solution for a nonlinear problem on compact d-dimensional () Riemannian manifolds without boundary, is established. More precisely, a recent critical point result for differentiable functionals is exploited, in order to prove the existence of a determined open interval of positive eigenvalues for which the considered problem admits at least one non-trivial weak solution. Moreover, as a consequence of our approach, a multiplicity result is presented, requiring the validity of the Ambrosetti-Rabinowitz hypothesis. Successively, the Cerami compactness condition is studied in order to obtain a similar multiplicity theorem in superlinear cases. Finally, applications to Emden-Fowler type equations are presented.
引用
收藏
页码:157 / 185
页数:29
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