Duffing Equation with Nonlinearities Between Eigenvalues

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F19%3A43956024" target="_blank" >RIV/49777513:23520/19:43956024 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/content/pdf/10.1007%2F978-3-030-26987-6_13.pdf" target="_blank" >https://link.springer.com/content/pdf/10.1007%2F978-3-030-26987-6_13.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-030-26987-6_13" target="_blank" >10.1007/978-3-030-26987-6_13</a>

Result language
angličtina
Original language name
Duffing Equation with Nonlinearities Between Eigenvalues
Original language description
In this article, we investigate the periodic nonlinear second order ordinary differential equation with damping u''(x) + r (x) u'(x) + g(x, u(x)) = f (x) , x ∈ [0, 2π] , u(0) = u(2π) , u'(0) = u'(2π) , where g is a L1-Caratheodory function, r ∈ C([0, 2π]), r ', f ∈ L1(0, 2π). We obtain a solution to this problem if a quotient g(x,s)/s lies between 0, 1/4+ ˜r (x) and 1/4 + ˜r (x), 1 + ˜r (x) or in interval (n^2 + ˜r (x), (n + 1)^2 + ˜r (x)), n ∈ N, where ˜ r (x) =r (x)/4+ r (x)'/2 . We use variational method and suppose that for functions u = u(x, a) satisfying lima→±∞ u(x, a) = ±∞ the function F(s) = int_0^2π int_0^s [−r'(x)u(x, a) + g(x,u(x, a)) − f (x) ] da dx has a critical point.
Czech name
—
Czech description
—

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)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)