Multiplicity of solutions to a degenerate diffusion problem Original Research Article

In this paper it is shown that the Dirichlet problem View the MathML source in a ball View the MathML source, loses the property of uniqueness of positive solutions u under the sole condition View the MathML source as λ→+∞, with View the MathML source certain prefixed zero of f, provided p>k+1,k being the order of View the MathML source, what is in contrast with the so-called “nondegenerate case” p⩽k+1 where such hypothesis implies uniqueness. This also proves that a slightly stronger convergence condition for uniqueness introduced by the authors in a previous work cannot be relaxed.