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Nonnegative solutions of nonlinear integral equations. (English) Zbl 0840.45007

The author proves some existence theorems for nonnegative solutions of two asymptotically linear, nonlinear integral equations, given by \[ p \bigl( x,u(x) \bigr) = \int^1_0q \bigl( x,t,u(t) \bigr) dt,\;x \in [0,1], \]
\[ p \bigl( x,u(x) \bigr) = m \left( x, \int^1_0 K(x,t) u(t)dt \right),\;x \in[0,1]. \] His method is based on abstract existence results of the theory of pseudomonotone operators.

MSC:

45G10 Other nonlinear integral equations
45M20 Positive solutions of integral equations
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