The Dirichlet problem for the fourth order nonlinear ordinary differential equations at resonance

0534402 - MÚ 2021 RIV AM eng J - Journal Article
Mukhigulashvili, Sulkhan - Manjikashvili, M.
The Dirichlet problem for the fourth order nonlinear ordinary differential equations at resonance.
Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences. Roč. 55, č. 5 (2020), s. 291-302. ISSN 1068-3623. E-ISSN 1934-9416
Institutional support: RVO:67985840
Keywords : Dirichlet problem * nonlinear ordinary differential equations
OECD category: Applied mathematics
Impact factor: 0.318, year: 2020
Method of publishing: Limited access
https://doi.org/10.3103/S1068362320050039

Landesman-Lazer’s type efficient sufficient conditions are established for the solvability of the two-point boundary value problem u(4) (t)=p(t)u(t)+f(t,u(t))+h(t) for a≤t≤b, u(i)(a)=0, u(i)(b)=0,(i=0,1), where h,p∈L([a,b],R) and f∈K([a,b]×R,R), in the case where the linear problem w(4)(t)=p(t)w(t), w(i)(a)=0, w(i)(b)=0, (i=0,1) has nontrivial solutions. The results obtained in the paper are optimal in the sense that if f≡0, i.e. when nonlinear equation turns to the linear equation, from our results follows the first part of Fredholm’s theorem.
Permanent Link: http://hdl.handle.net/11104/0312599