An elliptic equation on n-dimensional manifolds

Abstract

We consider an elliptic equation driven by a p-Laplacian-like operator, on an n-dimensional Riemannian manifold. The growth condition on the right-hand side of the equation depends on the geometry of the manifold. We produce a nontrivial solution by using a Palais–Smale compactness condition and a mountain pass geometry.

COMMUNICATED BY:

• V. R$\breve{\mathrm{a}}$dulescu

Keywords:

• Isocapacitary inequality
• mountain pass geometry
• Orlicz space
• p-Laplacian-like operator
• Sobolev space

AMS SUBJECT CLASSIFICATIONS:

• 35J20
• 58J05

Disclosure statement

No potential conflict of interest was reported by the author(s).