| Abstract: |
| We study positive radial solutions for a Dirichlet problem associated with a class of quasilinear $p$-Laplace differential equations involving a critical weighted nonlinearity. We show that the existence and multiplicity of solutions exhibit a bifurcation phenomenon depending on the flatness order of the weight at zero.
The existence of a second solution is new, even in the classical Laplace case.
The analysis is based on a dynamical systems approach via the Fowler transformation, and the main technical contribution consists in the construction of an unstable manifold in a non-smooth setting. |
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