## 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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### References:

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