Nehari manifold for degenerate logistic parabolic equations
In this article we analyze the behavior of solutions to a degenerate logistic equation with a nonlinear term $b(x)f(u)$ where the weight function $b$ is non-positive. We use variational techniques and the comparison principle to study the evolutionary dynamics. A crucial role is then played by the...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2025-06-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2025/60/abstr.html |
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| Summary: | In this article we analyze the behavior of solutions to
a degenerate logistic equation with a nonlinear
term $b(x)f(u)$ where the weight function $b$ is non-positive.
We use variational techniques and the comparison
principle 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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| ISSN: | 1072-6691 |