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\(\varvec{p}\)-Laplacian problems involving critical Hardy–Sobolev exponents

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Abstract

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

Keywords

p-Laplacian problems Critical Hardy–Sobolev exponents Existence Multiplicity Bifurcation Critical point theory Cohomological index Pseudo-index 

Mathematics Subject Classification

Primary 35J92 35B33 Secondary 35J20 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematical SciencesFlorida Institute of TechnologyMelbourneUSA
  2. 2.Department of Mathematical SciencesTsinghua UniversityBeijingChina

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