Advanced Topics in Semilinear Elliptic BVP

John M. Neuberger ()
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John M. Neuberger: Northern Arizona University, Department of Mathematics and Statistics

Chapter Chapter 5 in Difference Matrices for ODE and PDE, 2023, pp 181-201 from Springer

Abstract: Summary We lightly introduce a few more advanced topics concerning semilinear elliptic BVP. In particular, we introduce four algorithms for finding solutions of semilinear elliptic BVP. The tangent Newton method is used for branch following. The secant method is used for bifurcation detection. The mountain pass and modified mountain pass algorithms are used for finding the Morse index one and two solutions. We also compute solutions for fully nonlinear equations involving the p-Laplacian.

Date: 2023
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DOI: 10.1007/978-3-031-12000-8_5

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