This work demonstrates the uniqueness and multiplicity of positive solutions in nonlinear diffusion equations, indicating significant influence from degeneracies.
In this work, we consider a reaction–diffusion that combines nonlinear diffusion with degeneracies. By employing the sub- and supersolution method with bifurcation theorems and variational techniques, we establish several results on the existence, uniqueness, and multiplicity of positive solutions. Our results show that the structure of positive solutions is significantly affected by the pattern of the degeneracies.
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Cintra et al. (2026) studied this question.
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