In this paper, we deal with positive solutions for singular quasilinear problems whose model is {-Delta u + vertical bar del u vertical bar(2)/(1 - u)(gamma) = g in Omega, u = 0 on partial derivative Omega, where Omega is a bounded open set of R(N), g >= 0 is a function in some Lebesgue space, and gamma > 0. We prove both existence and nonexistence of solutions depending on the value of gamma and on the size of g.

Quasilinear elliptic equations with singular quadratic growth terms / Boccardo, Lucio; Leonori, Tommaso; Orsina, Luigi; Petitta, Francesco. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - STAMPA. - 13:4(2011), pp. 607-642. [10.1142/s0219199711004300]

Quasilinear elliptic equations with singular quadratic growth terms

BOCCARDO, Lucio;LEONORI, TOMMASO;ORSINA, Luigi;PETITTA, FRANCESCO
2011

Abstract

In this paper, we deal with positive solutions for singular quasilinear problems whose model is {-Delta u + vertical bar del u vertical bar(2)/(1 - u)(gamma) = g in Omega, u = 0 on partial derivative Omega, where Omega is a bounded open set of R(N), g >= 0 is a function in some Lebesgue space, and gamma > 0. We prove both existence and nonexistence of solutions depending on the value of gamma and on the size of g.
2011
nonlinear elliptic equations; natural growth condition; vertical asymptote; measure data
01 Pubblicazione su rivista::01a Articolo in rivista
Quasilinear elliptic equations with singular quadratic growth terms / Boccardo, Lucio; Leonori, Tommaso; Orsina, Luigi; Petitta, Francesco. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - STAMPA. - 13:4(2011), pp. 607-642. [10.1142/s0219199711004300]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/225272
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