The Nehari manifold for a degenerate logistic parabolic equation

Juliana Fernandes; Liliane A. Maia

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arXiv · 2303.08298

The Nehari manifold for a degenerate logistic parabolic equation

Juliana Fernandes·Liliane A. Maia

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Abstract

The present paper analyses the behavior of solutions to a degenerate logistic equation with a nonlinear term of the form b(x)f(u), where the weight function b is assumed to be nonpositive. We exploit variational techniques and comparison principle in order to study the evolutionary dynamics. A crucial role is then played by the Nehari manifold, as we note how it changes as the parameter {\lambda} in the equation or the function b vary, affecting the existence and non-existence of stationary solutions. We describe a detailed picture of the positive dynamics and also address the local behavior of solutions near a nodal equilibrium, which sheds some further light on the study of the evolution of sign-changing solutions.

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Juliana Fernandes, Liliane A. Maia. 2023-03-15. The Nehari manifold for a degenerate logistic parabolic equation. https://arxiv.org/abs/2303.08298

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