a study of nonlinear problems for the p-laplacian in rn via ricceri’s principle

in this paper, we consider the following nonlinear eigenvalue problems for the p-laplacian:

−div(a(x)|∇u|p−2 ∇u)= λ f (x, u) + μg(x, u) in rⁿ

λ,μ > 0, lim_|x|→∞u = 0,

where 1 < p < n, λ,μ > 0, a is a measurable bounded function, and f and g are nonlinearities having subcritical growth with respect to u. we prove multiple nontrivial solutions using a recent principle of ricceri (2009). a regularity result is also established.