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

Fečkan, Michal

Commentat. Math. Univ. Carol. 36, No. 4, 615-627 (1995).

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.

Reviewer: I.Schragin (Tübingen)

MSC:

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

Keywords:

nonnegative solutions; asymptotically linear, nonlinear integral equations; pseudomonotone operators