Open Access
Translator Disclaimer
1999 Existence and uniqueness of solutions of some abstract degenerate nonlinear equations
Angelo Favini, Anatoliy Rutkas
Differential Integral Equations 12(3): 373-394 (1999).


The nonlinear abstract differential equation $$ \frac{d}{dt}(Ay)+By(t)=F(t,Ky),\quad 0\le t\le\tau, $$ where $A,B,K$ are linear closed operators from a complex Banach space $Y$ into a Banach space $X$ is considered. The main assumption reads that the point $\xi =0$ is a polar singularity of the resolvent $(T-\xi I)^{-1}$, where $T=A(\lambda A+B)^{-1}$, $\lambda$ being a regular point of the operator pencil $\lambda A+B$. Mainly the case of a simple pole and of a second order pole are considered. Some examples of application to concrete partial differential equations are given. In particular, we show that the results work for mathematical models of nonlinear electrical networks.


Download Citation

Angelo Favini. Anatoliy Rutkas. "Existence and uniqueness of solutions of some abstract degenerate nonlinear equations." Differential Integral Equations 12 (3) 373 - 394, 1999.


Published: 1999
First available in Project Euclid: 29 April 2013

zbMATH: 1014.35047
MathSciNet: MR1674394

Primary: 34G20
Secondary: 34A09 , 35K99 , 47J05 , 47N20

Rights: Copyright © 1999 Khayyam Publishing, Inc.


Vol.12 • No. 3 • 1999
Back to Top