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| Critical Perturbation Results for a Mixed Boundary Value Problem |
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Citation： |
Azeb ALGHANEMI,Hichem CHTIOUI,Moctar MOHAMEDEN.Critical Perturbation Results for a Mixed Boundary Value Problem[J].Chinese Annals of Mathematics B,2025,46(1):25~50 |
| Page view： 177
Net amount： 149 |
Authors： |
Azeb ALGHANEMI; Hichem CHTIOUI;Moctar MOHAMEDEN |
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| Abstract： |
Let K be a given positive function on a bounded domain ? of Rn, n ≥ 3. The
authors consider a nonlinear variational problem of the form: ??u = K|u| 4/n?2 u in ? with
mixed Dirichlet-Neumann boundary conditions. It is a non-compact variational problem,
in the sense that the associated energy functional J fails to satisfy the Palais-Smale condition. This generates concentration and blow-up phenomena. By studying the behaviors
of non-precompact flow lines of a decreasing pseudogradient of J, they characterize the
points where blow-up phenomena occur, the so-called critical points at infinity. Such a
characterization combined with tools of Morse theory, algebraic topology and dynamical
system, allow them to prove critical perturbation results under geometrical hypothesis on
the boundary part in which the Neumann condition is prescribed. |
Keywords： |
Critical elliptic equations Variational methods Asymptotic analyzes Critical points at infinity |
Classification： |
35J20 |
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