Resumen de Existence of Positive Solutions for (N, p)-Laplace Equation with Exponential Nonlinearity Term and Convection Term in Dimension N

Wei Liu

• In this paper, we study the the following problem ⎧⎩⎨⎪⎪−ΔNu−μΔpu=λ(ur+a|∇u|s)+f(x,u)u>0u=0inΩ,inΩ,on∂Ω.

  (0.1) The term f could be exponential growth at +∞. The convection term involved with ∇u makes the problem (0.1) nonvariational and the variational methods are not applicable. Under suitable conditions imposed on f, the approximation scheme is employed to obtain the existence of positive solutions for all λ∈(0,λ∗] with λ∗>0.