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Full-Text Articles in Other Mathematics
Radial Singular Solutions To Semilinear Partial Differential Equations, Marcelo A. Almora Rios
Radial Singular Solutions To Semilinear Partial Differential Equations, Marcelo A. Almora Rios
HMC Senior Theses
We show the existence of countably many non-degenerate continua of singular radial solutions to a p-subcritical, p-Laplacian Dirichlet problem on the unit ball in R^N. This result generalizes those for the 2-Laplacian to any value p and extends recent work on the p-Laplacian by considering solutions both radial and singular.
Radial Solutions To Semipositone Dirichlet Problems, Ethan Sargent
Radial Solutions To Semipositone Dirichlet Problems, Ethan Sargent
HMC Senior Theses
We study a Dirichlet problem, investigating existence and uniqueness for semipositone and superlinear nonlinearities. We make use of Pohozaev identities, energy arguments, and bifurcation from a simple eigenvalue.
Best Approximations, Lethargy Theorems And Smoothness, Caleb Case
Best Approximations, Lethargy Theorems And Smoothness, Caleb Case
CMC Senior Theses
In this paper we consider sequences of best approximation. We first examine the rho best approximation function and its applications, through an example in approximation theory and two new examples in calculating n-widths. We then further discuss approximation theory by examining a modern proof of Weierstrass's Theorem using Dirac sequences, and providing a new proof of Chebyshev's Equioscillation Theorem, inspired by the de La Vallee Poussin Theorem. Finally, we examine the limits of approximation theorem by looking at Bernstein Lethargy theorem, and a modern generalization to infinite-dimensional subspaces. We all note that smooth functions are bounded by Jackson's Inequalities, but …
My Finite Field, Matthew Schroeder
My Finite Field, Matthew Schroeder
Journal of Humanistic Mathematics
A love poem written in the language of mathematics.