Existence of a renormalized solution of a quasilinear elliptic equation without the sign condition on the lower-order term. (English. Russian original) Zbl 07917704
Differ. Equ. 60, No. 6, 729-750 (2024); translation from Differ. Uravn. 60, No. 6, 764-785 (2024).
Summary: The paper considers a second-order quasilinear elliptic equation with an integrable right-hand side. Restrictions on the structure of the equation are stated in terms of the generalized \(N \)-function. Unlike the author’s previous papers, there is no sign condition on the lower-order term of the equation. The existence of a renormalized solution of the Dirichlet problem for this equation is proved in nonreflexive Musielak-Orlicz-Sobolev spaces in an arbitrary unbounded strictly Lipschitz domain.
Keywords:
quasilinear elliptic equation; unbounded domain; Musielak-Orlicz space; renormalized solution; existence of solutionReferences:
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