Existence and bifurcation results for fourth order elliptic equations involving two critical Sobolev exponents

Δημοσίευση σε επιστημονικό περιοδικόSummarization: Let be a smooth bounded domain inRN, withN≥5. We provide existence and bifurcation results for the elliptic fourth-order equation2u−pu= f(λ,x,u)in, under the Dirichlet boundary conditionsu=0and∇u= 0. Hereλ is a positive real number, 1<p≤2# and f(., .,u) has a subcritical or a critical growth s, 1< s≤2∗, where 2∗ := 2N N−4 and 2# := 2N N−2. Our approach is variational, and it is based on the mountain-pass theorem, the Ekeland variational principle and the concentration-compactness principle.Presented on: Glasgow Mathematical Journa