Abstract
Certain equations in function space, including boundary value problems for nonlinear differential equations involving a parameter, may have multiple solutions near a given one. The problem of counting the number of solutions near a given solution has been treated by several writers (see, for example, Schmidt [7], Iglisch [5; 6], Cronin [2; 3; 4,], Bartle [1]), but no method has been devised which will give a definite count in all cases. The problems we are discussing may be subsumed under the general one of determining the number of solutions x =x(y) near x = 0, y = 0, of an equation
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