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Advanced Topics in Semilinear Elliptic BVP

In: Difference Matrices for ODE and PDE

Author

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  • John M. Neuberger

    (Northern Arizona University, Department of Mathematics and Statistics)

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.

Suggested Citation

  • John M. Neuberger, 2023. "Advanced Topics in Semilinear Elliptic BVP," Springer Books, in: Difference Matrices for ODE and PDE, chapter 0, pages 181-201, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-12000-8_5
    DOI: 10.1007/978-3-031-12000-8_5
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