Numerical methods for finding multiple solutions of a logistic equation. (English) Zbl 1117.65150
Summary: Using numerical methods, we show the existence of multiple solutions for the well known logistic equation \(-\Delta u = \lambda g(x)u(1 - u)\) for x \(\in \Omega\), with Dirichlet boundary condition.
MSC:
| 65N25 | Numerical methods for eigenvalue problems for boundary value problems involving PDEs |
| 35P30 | Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs |
| 35J65 | Nonlinear boundary value problems for linear elliptic equations |
| 92D25 | Population dynamics (general) |
Keywords:
sub- and super-solutions; logistic equation; multiple positive solutions; mountain pass Lemma; semilinear eigenvalue problem; numerical examplesReferences:
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