Advances in Differential Equations

Asymptotic profile of $2$-nodal solutions to a semilinear elliptic problem on a Riemannian manifold

Mónica Clapp and Anna Maria Micheletti

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We describe the asymptotic profile of sign changing solutions with small energy to the singularly perturbed nonlinear elliptic equation $-\varepsilon ^{2}\Delta_{g}u+u=|u|^{p-2}u$ on an $n$-dimensional compact Riemannian manifold $M$ without boundary, $p\in(2,2^{\ast}),$ as $\varepsilon \rightarrow0.$

Article information

Source
Adv. Differential Equations Volume 19, Number 3/4 (2014), 225-244.

Dates
First available in Project Euclid: 30 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.ade/1391109085

Mathematical Reviews number (MathSciNet)
MR3161661

Zentralblatt MATH identifier
1296.58010

Subjects
Primary: 58J05: Elliptic equations on manifolds, general theory [See also 35-XX] 35B25: Singular perturbations 35J61: Semilinear elliptic equations 35R01: Partial differential equations on manifolds [See also 32Wxx, 53Cxx, 58Jxx] 55R12: Transfer 55R80: Discriminantal varieties, configuration spaces

Citation

Clapp, Mónica; Micheletti, Anna Maria. Asymptotic profile of $2$-nodal solutions to a semilinear elliptic problem on a Riemannian manifold. Adv. Differential Equations 19 (2014), no. 3/4, 225--244. https://projecteuclid.org/euclid.ade/1391109085.


Export citation