On the Morse index of least energy nodal solutions for quasilinear elliptic problems
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F20%3A43958477" target="_blank" >RIV/49777513:23520/20:43958477 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00526-020-1730-x" target="_blank" >https://doi.org/10.1007/s00526-020-1730-x</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00526-020-1730-x" target="_blank" >10.1007/s00526-020-1730-x</a>
Alternative languages
Result language
angličtina
Original language name
On the Morse index of least energy nodal solutions for quasilinear elliptic problems
Original language description
In this paper we study the quasilinear equation −ε2Δu−Δpu=f(u) in a smooth bounded domain Ω⊂RN with Dirichlet boundary condition, where p>2 and f is a suitable subcritical and p-superlinear function at ∞. First, for ϵ≠0 we prove that Morse index is two for every least energy nodal solution. This result is inspired and motivated by previous results by A. Castro, J. Cossio and J. M. Neuberger, and T. Bartsch and T. Weth; and it is connected with a result by S. Cingolani and G. Vannella. Then, for the limit case ε=0 we prove (a) the existence of a least energy nodal solution whose Morse index is two, and (b) Morse index is two for every nodal solution which strictly and locally minimizes the energy functional on the set of sign-changing admissible functions.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Calculus of Variations and Partial Differential Equations
ISSN
0944-2669
e-ISSN
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Volume of the periodical
59
Issue of the periodical within the volume
2
Country of publishing house
DE - GERMANY
Number of pages
35
Pages from-to
1-35
UT code for WoS article
000519074900001
EID of the result in the Scopus database
2-s2.0-85081013393