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Radially symmetric solutions of a class of singular elliptic equations

  • Juan A. Gatica (a1), Gaston E. Hernandez (a1) and P. Waltman (a2)

Abstract

The boundary value problem

is studied with a view to obtaining the existence of positive solutions in C1([0, 1])∩C2((0, 1)). The function f is assumed to be singular in the second variable, with the singularity modeled after the special case f(x, y) = a(x)yp, p>0.

This boundary value problem arises in the search of positive radially symmetric solutions to

where Ω is the open unit ball in ℝN, centered at the origin, Γ is its boundary and |x| is the Euclidean norm of x.

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References

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1.Atkinson, F. V. and Peletier, L. A., Ground states of −Δu = f(u) and the Emden–Fowler equation, Arch. Rational Mech. Anal. 93 (1986), 103107.
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Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
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