Nonlinear periodic problems superlinear at $+\infty$ and sublinear at $-\infty$
Sergiu Aizicovici, Νικόλαος Παπαγεωργίου, Vasile Staicu · LIBERTAS MATHEMATICA (new series) · 2013
We consider a nonlinear periodic problem driven by a nonlinear, nonhomogeneous differential operator with a reaction which exhibits an asymmetric growth at $+\infty$ and at $-\infty$. It is $\left( p-1\right) -$superlinear near $+\infty$ and $\left( p-1\right) -$ sublinear near $-\infty$. A particular case of our problem is that of periodic equations with the scalar $p-$ Laplacian and an asymmetric nonlinearity. Using variational methods and Morse theory, we prove the existence of at least three nontrivial solutions.