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In this work, we are concerned with a nonlocal boundary value problem of nonhomogeneous Sturm-Liouville equation. Then existence of at least one solution will be proved. The spectral properties of the problem will be studied. The multiple solutions of the nonhomogeneous equation with the nonlocal boundary condition will be given. AMS Subject Classification: 34A55, 34B10, 34B15, 34B18, 34L10, 34L40, 34K10

ON THE MULTIPLE SOLUTIONS OF A NONHOMOGENEOUS STURM-LIOUVILLE EQUATION WITH NONLOCAL BOUNDARY CONDITIONS