Nonlinear eigenvalue problems for some degenerate
elliptic operators on $\mathbb R^N$

Mihăilescu, Mihai

Nonlinear eigenvalue problems for some degenerate elliptic operators on $\mathbb R^N$

Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2005) no. 5, p. 435-448 / Harvested from Project Euclid

Résumé

We study two nonlinear degenerate eigenvalue problems on $\mathbb R^N$. For the first problem we prove the existence of a positive eigenvalue while for the second we show the existence of a continuous family of eigenvalues. Our approach is based on standard tools in the critical point theory combined with adequate variational methods. We also apply an idea developed recently by Szulkin and Willem.

Publié le : 2005-09-14
Classification: degenerate elliptic equation, singular potential, eigenvalue problem, weak solution, 35J60, 35J25, 35J70

@article{1126195347,
     author = {Mih\u ailescu, Mihai},
     title = {Nonlinear eigenvalue problems for some degenerate
elliptic operators on $\mathbb R^N$},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {11},
     number = {5},
     year = {2005},
     pages = { 435-448},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1126195347}
}

Mihăilescu, Mihai. Nonlinear eigenvalue problems for some degenerate
elliptic operators on $\mathbb R^N$. Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2005) no. 5, pp.  435-448. http://gdmltest.u-ga.fr/item/1126195347/