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<p>Abstract</p> <p>We discuss Neumann and Robin problems driven by the <inline-formula> <graphic file="1687-2770-2011-214289-i2.gif"/></inline-formula>-Laplacian with jumping nonlinearities. Using sub-sup solution method, Fuc&#237;k spectrum, mountain pass theorem, degree theorem together with suitable truncation techniques, we show that the Neumann problem has infinitely many nonconstant solutions and the Robin problem has at least four nontrivial solutions. Furthermore, we study oscillating equations with Robin boundary and obtain infinitely many nontrivial solutions.</p>