On the solvability of asymptotically linear systems at resonance

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F16%3A43929891" target="_blank" >RIV/49777513:23520/16:43929891 - isvavai.cz</a>
Result on the web
<a href="http://www.sciencedirect.com/science/article/pii/S0022247X16301202" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0022247X16301202</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2016.04.066" target="_blank" >10.1016/j.jmaa.2016.04.066</a>

Result language
angličtina
Original language name
On the solvability of asymptotically linear systems at resonance
Original language description
This paper is concerned with the solvability of the system-?u-?1?1v=f(x,u,v)+h1(x) in ? -?v-?1?2u=g(x,u,v)+h2(x) in ? u=v=0 on PARTIAL DIFFERENTIAL?, at resonance at the simple eigenvalue ?1 of the corresponding linear eigenvalue problem. Here ?SUBSET OFRN (NGREATER-THAN OR EQUAL TO1) is a bounded domain with C2,?-boundary PARTIAL DIFFERENTIAL?, ?ELEMENT OF(0, 1) (a bounded interval if N=1) and ?1, ?2 are positive constants. The nonlinear perturbations f(x,u,v),g(x,u,v):?xR2RIGHTWARDS ARROWR are Carathéodory functions that are sublinear at infinity. We employ the Lyapunov-Schmidt method to provide sufficient conditions on h1, h2ELEMENT OFLr(?); r>N, to guarantee the solvability of the system.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GA13-00863S" target="_blank" >GA13-00863S: Semilinear and Quasilinear Differential Equations: Existence and Multiplicity Results</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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