Differential and Integral Equations

Existence and uniqueness of solutions of some abstract degenerate nonlinear equations

Angelo Favini and Anatoliy Rutkas

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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.

Article information

Differential Integral Equations, Volume 12, Number 3 (1999), 373-394.

First available in Project Euclid: 29 April 2013

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34G20: Nonlinear equations [See also 47Hxx, 47Jxx]
Secondary: 34A09: Implicit equations, differential-algebraic equations [See also 65L80] 35K99: None of the above, but in this section 47J05: Equations involving nonlinear operators (general) [See also 47H10, 47J25] 47N20: Applications to differential and integral equations


Favini, Angelo; Rutkas, Anatoliy. Existence and uniqueness of solutions of some abstract degenerate nonlinear equations. Differential Integral Equations 12 (1999), no. 3, 373--394. https://projecteuclid.org/euclid.die/1367265217

Export citation