In this paper we study the existence and regularity of solutions to the following singular problemproving that the lower order term u|u| s−1 has some regularizing effects on the solutions in the case of an elliptic operator with degenerate coercivity.
In this paper, we establish the existence of weak solution in Orlicz-Sobolev space for the following Kirchhoff type probelmwhere Ω is a bounded subset in R N , N ≥ 1 with Lipschitz boundary ∂Ω.The used technical approach is mainly based on Leray-Shauder's non linear alternative.
We consider the following non-linear singular elliptic problem (1) − div ( M ( x ) | ∇ u | p − 2 ∇ u ) + b | u | r − 2 u = a u p − 1 | x | p + f u γ in Ω u > 0 in Ω u = 0 on ∂ Ω , where 1 < p < N; Ω ⊂ R N is a bounded regular domain containing the origin and 0 < γ < 1, a ⩾ 0 , b > 0 , 0 ⩽ f ∈ L m ( Ω ) and 1 < m < N p . The main goal of this work is to study the existence and regularizing effect of some lower order terms in Dirichlet problems despite the presence of Hardy the potentials and the singular term in the right hand side.
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