期刊
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
卷 60, 期 5, 页码 -出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s00526-021-02075-6
关键词
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资金
- CNPq [429955/2018-9, 309026/2020-2]
- CNPq/Brazil [311562/2020 -5]
The existence of minimal W-loc(1,Phi)(Omega)-solutions in an appropriate set for the quasilinear elliptic problem has been established. The study improves classical results in the presence of strongly-singular nonlinearities and gradient terms. The approach is based on a new comparison principle, truncation arguments, estimates and a generalized Galerkin method.
It is established existence of minimal W-loc(1,Phi)(Omega)-solutions on some appropriated set for the quasilinear elliptic problem [-Delta Phi u = lambda f(x, u) + mu h(x, u, del u) in Omega, u > 0 in Omega, u = 0 on partial derivative Omega, where f may have indefinite sign and behaves in a strongly singular way at u = 0, h has sublinear growth, lambda > 0 and mu >= 0 are real parameters. The main results improve the classical Brezis-Oswald's result to Orlicz-Sobolev setting in the presence of strongly-singular nonlinearities as well as gradient terms. Our approach is based on a new comparison principle for W-loc(1,Phi)(Omega)-sub and super solutions to the Phi-Laplacian operator established here, truncation arguments, L-infinity(Omega) estimates and a generalized Galerkin method.
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