Parameterized splitting theorems and bifurcations for potential operators, Part II: Applications to quasi-linear elliptic equations and systems

Guangcun Lu

doi:10.3934/dcds.2021155

Article Contents

2022, Volume 42, Issue 3: 1317-1368. Doi: 10.3934/dcds.2021155

This issue Previous Article Parameterized splitting theorems and bifurcations for potential operators, Part I: Abstract theory Next Article Elliptic systems involving Schrödinger operators with vanishing potentials

Parameterized splitting theorems and bifurcations for potential operators, Part II: Applications to quasi-linear elliptic equations and systems

Guangcun Lu

School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China

Received: April 2021

Early access: October 2021

Published: March 2022

Partially supported by the NNSF 11271044 of China

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Abstract

This is the second part of a series devoting to the generalizations and applications of common theorems in variational bifurcation theory. Using abstract theorems in the first part we obtain many new bifurcation results for quasi-linear elliptic boundary value problems of higher order.

Keywords:

Bifurcation,
quasi-linear elliptic Euler equations.

Mathematics Subject Classification: Primary: 35B32; Secondary: 58J55, 35J35.

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