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This paper deals with the second-order nonlinear differential equation [Formula: see text] involving [Formula: see text]-Laplacian. The existence and the uniqueness of nonoscillatory solutions of this equation in certain classes, which are related with integral conditions, are studied. Moreover, a minimal set for solutions of this equation is introduced as an extension of the concept of principal solutions for linear equations. Obtained results extend the results for equations with [Formula: see text]-Laplacian.