A study of nonlinear problems for the pp-Laplacian in RnRn via Ricceri’s principle

In this paper, we consider the following nonlinear eigenvalue problems for the pp-Laplacian: View the MathML source−div(a(x)|∇u|p−2∇u)=λf(x,u)+μg(x,u)in Rn Turn MathJax on View the MathML sourceλ,μ>0,lim|x|→∞u=0, Turn MathJax on where 10λ,μ>0, aa is a measurable bounded function, and ff and gg are nonlinearities having subcritical growth with respect to uu. We prove multiple nontrivial solutions using a recent principle of Ricceri (2009) [10]. A regularity result is also established.