phuong lien Le - Academia.edu (original) (raw)
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Papers by phuong lien Le
Differential Equations & Applications, 2012
Using a recent fixed point theorem in ordered Banach spaces by S. Carl and S. Heikkilä, we study ... more Using a recent fixed point theorem in ordered Banach spaces by S. Carl and S. Heikkilä, we study the existence of weak solutions to nonlinear elliptic problems −diva(x,∇u) = f (x,u) in a bounded domain Ω ⊂ R n with Dirichlet boundary condition. In particular, we prove that for some suitable function g , which may be discontinuous, and δ small enough, the p-Laplace equation −div(|∇u| p−2 ∇u) = |u| p * −2 u + δ g(x,u) has a positive solution which goes to 0 as δ → 0 + , where p * is the critical exponent.
Differential Equations & Applications, 2012
Using a recent fixed point theorem in ordered Banach spaces by S. Carl and S. Heikkilä, we study ... more Using a recent fixed point theorem in ordered Banach spaces by S. Carl and S. Heikkilä, we study the existence of weak solutions to nonlinear elliptic problems −diva(x,∇u) = f (x,u) in a bounded domain Ω ⊂ R n with Dirichlet boundary condition. In particular, we prove that for some suitable function g , which may be discontinuous, and δ small enough, the p-Laplace equation −div(|∇u| p−2 ∇u) = |u| p * −2 u + δ g(x,u) has a positive solution which goes to 0 as δ → 0 + , where p * is the critical exponent.