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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.

MSC:

47J25 Iterative procedures involving nonlinear operators
47H05 Monotone operators and generalizations
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