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Some Existence Results for a Singular Elliptic Problem via Bifurcation Theory
Full text linkWe study a semilinear elliptic problem with a singular nonlinear term of the
type , using a variational approach. Note that the minus sign is
important since the corresponding term in the Euler-Lagrange functional is
concave. Contrary to the convex case there are no solutions for the Dirichlet
problem, due to the power being . We therefore study the Neumann problem
and prove a local existence result for solutions bifurcating from constant
solutions. In the radial case we show that one of the two bifurcation branches
is global and unbounded, and we find its asympotic behaviour.Comment: There is a significant problem in the proof of Theorem 2.1: the
"classical bifurcation result for potential operators" quoted at the end of
the proof of 2.1 seems not to be so well known and the cited paper [8] only
covers a very partial case . So a major revision was needed and the author
has came to the conclusion that the revised version should be a new paper,
with a different titl
Eigenvalue problems for some variational inequalities with pointwise gradient constraints
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Multiple Positive Solutions for a Nonsymmetric Elliptic Problem with Concave Convex NonlinearityAnalysis and Topology in Nonlinear Differential Equations
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