On a dirichlet problem with a singular nonlinearity

We establish some bifurcation results for the boundary value problem −∆u = g(u)where Ω is a smooth bounded domain in R N , λ, µ ≥ 0, 0 < p ≤ 2, f is nondecreasing with respect to the second variable, and g is unbounded around the origin. The asymptotic behaviour of the solution around the bifurcation point is also established, provided g(u) behaves like u −α around the origin, for some 0 < α < 1. Our approach relies on finding explicit sub-and super-solutions combined with various techniques related to the maximum principle for elliptic equations. The analysis we develop in this paper shows the key role played by the convection term |∇u| p .

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“…2) has a unique solution (see [14,29]). When µ > 0, the study of (1.2) emphasizes the role played by the nonlinear term f (x, u).…”

Section: Introduction and The Main Resultsmentioning

confidence: 99%

Multi-parameter bifurcation and asymptotics for the singular Lane–Emden–Fowler equation with a convection term

Ghergu

Rădulescu

2005

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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“…In the case N -1 , this problem arises in certain applications in fluid mechanics and pseudoplastic flow (see [5,6,7]). The /V-dimensional problem (1.1)-(1.2) has been studied in [2] for general regions. In [2], it is shown that solutions exist if Q, is C3, and estimates are given for the behaviour of the solution as the boundary of Q is approached.…”

Section: Introductionmentioning

confidence: 99%