A boundary value problem on the unit disk in R2 is considered, involving an elliptic operator with a singular weight of logarithmic type and nonlinearities which are subcritical or critical with respect to the as- sociated gradient norm. The existence of non-trivial solutions is proved, relying on variational methods. In the critical case, the associated ener- gy functional is non-compact. A suitable asymptotic condition allows to avoid the non-compactness levels of the functional.

Elliptic equations in dimension 2 with double exponential nonlinearities / M. Calanchi, B. Ruf, F. Sani. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - 24:3(2017 Jun), pp. 29.1-29.18. [10.1007/s00030-017-0453-y]

Elliptic equations in dimension 2 with double exponential nonlinearities

M. Calanchi
Primo
;
B. Ruf
Secondo
;
F. Sani
Ultimo
2017

Abstract

A boundary value problem on the unit disk in R2 is considered, involving an elliptic operator with a singular weight of logarithmic type and nonlinearities which are subcritical or critical with respect to the as- sociated gradient norm. The existence of non-trivial solutions is proved, relying on variational methods. In the critical case, the associated ener- gy functional is non-compact. A suitable asymptotic condition allows to avoid the non-compactness levels of the functional.
Trudinger–Moser type inequalities; Critical exponents
Settore MAT/05 - Analisi Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/504795
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