Multiple critical points of saddle geometry functionals

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F18%3A43950550" target="_blank" >RIV/49777513:23520/18:43950550 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.na.2018.01.008" target="_blank" >https://doi.org/10.1016/j.na.2018.01.008</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.na.2018.01.008" target="_blank" >10.1016/j.na.2018.01.008</a>

Result language
angličtina
Original language name
Multiple critical points of saddle geometry functionals
Original language description
We study the multiplicity of critical points for continuously differentiable functionals on real Banach spaces. We prove that a functional which satisfies the assumptions of the Saddle Point Theorem and moreover is bounded from below has at least three critical points. Apparently, there is a global minimizer and a saddle point and we show the existence of a third critical point. The idea of the proof is based on the minus-gradient flow. This result is closely related to the three critical points theorem of H. Brezis and L. Nirenberg which assumes a local linking. Finally, we apply the result on the Dirichlet problem for semilinear stationary PDEs. The analysis includes, for example, the existence of multiple stationary solutions of bistable (or Allen–Cahn) equation and semipositone problems.
Czech name
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Czech description
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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

Project
<a href="/en/project/LO1506" target="_blank" >LO1506: Sustainability support of the centre NTIS - New Technologies for the Information Society</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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