Exact Multiplicity of Positive Solutions for a Quasilinear Boundary Value Problem with Density-Dependent Diffusion and Bistable Nonlinearity
DOI:
https://doi.org/10.22399/ijcesen.5257Keywords:
p-Laplacian, Positive solutions, p-Laplacian Time-map, Nonlinear diffusion, BistabilityAbstract
We investigate the exact number of positive solutions for a quasilinear Dirichlet problem with a density-dependent diffusion coefficient of the form and a bistable nonlinearity , where , , , , . Using the quadrature (time-map) method, we determine the exact multiplicity of positive solutions for all . For , we identify two critical values such that the problem admits zero, one, or exactly two solutions depending on . The paper also includes a physical interpretation of the parameters and a numerical illustration of the theoretical results for .
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