Resonance Problems For Quasilinear Elliptic Equations

Consider the quasilinear elliptic equations with Dirichlet boundary condition in iland the quasilinear elliptic equations with nonlinear boundary conditionwhere is the quasilinear elliptic mapping with p > 1, λ∈R Ω is a smooth domain in R^N, and is the outer normal derivative. Suppose is a continuous function satisfyingDefineIf A is the corresponding eigenvalue in (1) or (2), we say (1)(3) or (2)(3) is resonance problem.The existence of weak solutions in (1) and (2) are obtained by applying the variational approach. The main results are following:Theorem 1 Assume il is a bounded domain in R^N, h(x) = a(x) = 1, g₀ ∈ C{R, R) satisfies (3), and f₀ ∈ L^p'(Ω)(p' = p/(p-1)) satisfies...