# $$\varvec{p}$$ p -Laplacian problems involving critical Hardy–Sobolev exponents

$$\varvec{p}$$ p -Laplacian problems involving critical Hardy–Sobolev exponents We prove existence, multiplicity, and bifurcation results for p-Laplacian problems involving critical Hardy–Sobolev exponents. Our results are mainly for the case $$\lambda \ge \lambda _1$$ λ ≥ λ 1 and extend results in the literature for $$0< \lambda < \lambda _1$$ 0 < λ < λ 1 . In the absence of a direct sum decomposition, we use critical point theorems based on a cohomological index and a related pseudo-index. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Differential Equations and Applications NoDEA Springer Journals

# $$\varvec{p}$$ p -Laplacian problems involving critical Hardy–Sobolev exponents

, Volume 25 (3) – Jun 4, 2018
16 pages

/lp/springer_journal/varvec-p-p-laplacian-problems-involving-critical-hardy-sobolev-UKG1XSAFwr
Publisher
Springer International Publishing
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Analysis
ISSN
1021-9722
eISSN
1420-9004
D.O.I.
10.1007/s00030-018-0517-7
Publisher site
See Article on Publisher Site

### Abstract

We prove existence, multiplicity, and bifurcation results for p-Laplacian problems involving critical Hardy–Sobolev exponents. Our results are mainly for the case $$\lambda \ge \lambda _1$$ λ ≥ λ 1 and extend results in the literature for $$0< \lambda < \lambda _1$$ 0 < λ < λ 1 . In the absence of a direct sum decomposition, we use critical point theorems based on a cohomological index and a related pseudo-index.

### Journal

Nonlinear Differential Equations and Applications NoDEASpringer Journals

Published: Jun 4, 2018

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