On a class of parametric $(p,2)$-equations
  We consider parametric equations driven by the sum of a $p$-Laplacian and a Laplace operator (the so-called $(p,2)$-equations). We study the existence and multiplicity of solutions when the parameter $\lambda>0$ is near the principal eigenvalue $\hat{\lambda}_1(p)>0$ of $(-\Delta_p,W^{1,p}_{0}(\Omega))$. We prove multiplicity results with precise sign information when the near resonance occurs from above and from below of $\hat{\lambda}_1(p)>0$. 
Nikolaos S. Papageorgiou, Vicen\c{t}iu D. R\u{a}dulescu, and Du\v{s}an   D. Repov\v{s}
math.AP