Existence and multiplicity results for generalized logistic equations. (October 2016) - Huy, Nguyen Bich; Quan, Bui The; Khanh, Nguyen Huu
Abstract: We consider elliptic Dirichlet problem − Δ p u = λ f ( x, u, ∇ u ) − g ( x, u )  in  Ω, u = 0  on  ∂ Ω . Assume that the nonlinearity f satisfies certain growth condition. Using the fixed point index, the Leggett–Williams theorem on fixed point and the arguments on monotone minorant, we prove the existence and multiplicity results for the equation. This extends some known results.