On the existence of solutions of nonlinear equations. (English) Zbl 0861.47045
The author studies the solvability of the equation
\[
L(u)= N(u)+h
\]
in a Hilbert space \(H\). Here \(L\) is an asymptotically linear continuous map, and \(N\) is a so-called asymptotically quasilinear compact map. Applications are given for the functional-integral equation
\[
p(x,u(x))= \int^1_0 G(x,t) m(t,u(t))dt+ f(x)
\]
and some boundary value problem associated to this equation.
Reviewer: J.Appell (Würzburg)
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H05 | Monotone operators and generalizations |
Keywords:
asymptotically linear continuous map; asymptotically quasilinear compact map; functional-integral equation; boundary value problemReferences:
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