We study the existence of solutions of the nonlinear problem [GRAPHICS] where p is a bounded measure and g is a continuous nondecreasing function such that g(0) = 0. In this paper, we assume that the nonlinearity g satisfies [GRAPHICS] Problem (0.1) need not have a solution for every measure A. We prove that, given p, there exists a "closest" measure mu* for which (0.1) can be solved. We also explain how assumption (0.2) makes problem (0.1) different from the case where g(t) is defined for every t is an element of R.

Dupaigne, L., Ponce, A.C., & Porretta, A. (2006). Elliptic equations with vertical asymptotes in the nonlinear term. JOURNAL D'ANALYSE MATHEMATIQUE, 98, 349-396 [10.1007/BF02790280].

Elliptic equations with vertical asymptotes in the nonlinear term

PORRETTA, ALESSIO
2006

Abstract

We study the existence of solutions of the nonlinear problem [GRAPHICS] where p is a bounded measure and g is a continuous nondecreasing function such that g(0) = 0. In this paper, we assume that the nonlinearity g satisfies [GRAPHICS] Problem (0.1) need not have a solution for every measure A. We prove that, given p, there exists a "closest" measure mu* for which (0.1) can be solved. We also explain how assumption (0.2) makes problem (0.1) different from the case where g(t) is defined for every t is an element of R.
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/05 - Analisi Matematica
English
Dupaigne, L., Ponce, A.C., & Porretta, A. (2006). Elliptic equations with vertical asymptotes in the nonlinear term. JOURNAL D'ANALYSE MATHEMATIQUE, 98, 349-396 [10.1007/BF02790280].
Dupaigne, L; Ponce, A; Porretta, A
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/38894
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