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Showing 1 to 7 of 7 for “"semilinear elliptic equations"”.
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CLASSIFICATION RESULTS FOR SEMILINEAR ELLIPTIC EQUATIONS
… classification problems of solutions to semilinear elliptic equations, with a particular focus on the study of symmetry and rigidity results. The thesis is divided into four chapters. In Chapter 1 we consider solutions to some semilinear elliptic equations on complete noncompact …
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Symmetry properties of semilinear elliptic equations with isolated singularities
… symmetry properties for positive solutions of semilinear elliptic equations. We give a detailed proof of the result due to Caffarelli, Gidas, and Spruck that a solution in the punctured ball, B\{0}, behaves asymptotically like its spherical average at the origin. We also show that a solution …
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Blowing-up patterns in semilinear elliptic equations of critical type
Hay dos partes en mi tesis. La primera parte se dedica principalmente a la construcción de soluciones burbujeantes de algunos problemas elípticos con no linealidad exponencial en $\mathbb{R}^2$. En la segunda parte se considera la existencia de soluciones de punta para ecuaciones elípticas en …
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Existence of Solutions Via a New Variational Principle for Nonlocal Semilinear Elliptic Equations
… is to prove the existence of a weak solution for semilinear fractional elliptic equations given by \begin{eqnarray*}\left\{ \begin{array}{ll} (-\Delta)^s u=|u|^{p-2} u+ f(x),& \quad x\in \Omega,\\ u=0, & \quad x \in \R^n \backslash \Omega, %0, & \quad x \in \partial \Oemga, \end{array} \right. …
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Semilinear elliptic partial differential equations with the critical Sobolev exponent
… analysis are applied to solving certain types of semilinear elliptic partial differential equations (PDEs). The ultimate goal is to prove results on the existence and non-existence of solutions to the Semilinear Elliptic PDEs with the Critical Sobolev Exponent. To this end, we first recall some …
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Nonlinear Methods in the Study of Singular Partial Differential Equations
Nonlinear singular partial differential equations arise naturally when studying models from such areas as Riemannian geometry, applied probability, mathematical physics and biology. The purpose of this thesis is to develop analytical methods to investigate a large class of nonlinear elliptic PDEs …
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Travelling wave solutions of the heat equation in an unbounded cylinder with a non-linear boundary condition
… Finding such a solution amounts to solving the elliptic PDE $Delta u - c partial_x u = 0$ for $(x,y)inRimesOmega$ with $partial u over partial n = f(u)$ on $RimespartialOmega$. The main result is the existence of a non-trivial solution of this equation for a large class of non-linearities $f$. …