Abstract.
We consider here a class of nonlinear Dirichlet problems, in a bounded domain Ω, of the form
investigating the problem of uniqueness of solutions. The functions Φ(s) and \(s \mapsto a(x,s)\) satisfy rather general assumptions of locally Lipschitz continuity (with possibly exponential growth) and the datum f is in L1(Ω). Uniqueness of solutions is proved both for coercive a(x, s) and for the case of a(x, s) degenerating for s large.
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Porretta, A. Uniqueness of solutions for some nonlinear Dirichlet problems. Nonlinear differ. equ. appl. 11, 407–430 (2004). https://doi.org/10.1007/s00030-004-0031-y
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DOI: https://doi.org/10.1007/s00030-004-0031-y