Existence and nonexistence results for quasilinear elliptic equations involving the $p$-Laplacian

Abdellaoui, Boumediene ; Felli, Veronica ; Peral, Ireneo

Bollettino della Unione matematica italiana, Série 8, 9B (2006) no. 2, pp. 445-484.

Résumé

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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