Symmetric positive solutions for nonlocal boundary value problems of fourth order

Abstract: The singular fourth-order nonlocal boundary value problem is considered under some suitable conditions concerning the first eigenvalue of the corresponding linear operator, where is continuous, symmetric on (0, 1) and may be singular at and is continuous and is symmetric on [0,1] for all . The existence of at least one symmetric positive solution is obtained by the application of the fixed point index in cones. [Copyright &y& Elsevier]