Abdellaoui, Boumediene and Felli, Veronica and Peral, Ireneo:
Existence and nonexistence results for quasilinear elliptic equations involving the $p$-Laplacian
Bollettino dell'Unione Matematica Italiana Serie 8 9-B (2006), fasc. n.2, p. 445-484, (English)
pdf (407 Kb), djvu (334 Kb). | MR2233146 | Zbl 1118.35010
Sunto
L’articolo riguarda lo studio di un’equazione ellittica quasi-lineare con il p-laplaciano, caratterizzata dalla presenza di un termine singolare di tipo Hardy ed una nonlinearità critica. Si dimostrano dapprima risultati di esistenza e non esistenza per l’equazione con un termine singolare concavo. Quindi si passa a studiare il caso critico legato alla disuguaglianza di Hardy, fornendo una descrizione del comportamento delle soluzioni radiali del problema limite e ottenendo risultati di esistenza e molteplicità mediante metodi variazionali e topologici.
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