This paper deals primarily with solutions of (1) , , satisfying boundary conditions of the type (2) , , , , (3) , , , , (4) , , , , or (5) , , , , where may have singularities at and at , .
The first results concern problem (1), (2), where has singularities at , not at . Growth assumptions are made on such that one can conclude the existence of a priori bounds (independent of ), on solutions of , , , satisfying , , , . By applying the topological transversality theorem of Granas, one obtains a solution of (1), (2). Later, boundary value problems are treated similarly for , where has singularities at , and is positive and improper integrable over (0,1).
Boundary value problems for equation (1) with any of the conditions (3), (4), or (5) are dealt with similarly, and then in the last section, results are given for boundary problems for , , where, as above, may have singularities at and at , .