Infinitely Many Nodal Solutions for Nonlinear Nonhomogeneous Robin Problems

We consider a nonlinear Robin problem driven by a nonhomogeneous differential operator which incorporates the p -Laplacian as special case. The reaction <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>f</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>z</m:mi> <m:mo>,</m:mo> <m:mi>x</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> f(z,x) is a Carathéodory function which need not satisfy a global growth condition and is only assumed to be odd near zero. Using variational tools, we show that the problem has a whole sequence of distinct nodal (that is, sign-changing) solutions.