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Positive solutions obtained as local minima via symmetries, for nonlinear elliptic equations.

机译：对于非线性椭圆方程，通过对称获得的局部极小正解。

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In this dissertation, we establish existence and multiplicity of positive solutions for semilinear elliptic equations with subcritical and critical nonlinearities. We treat problems invariant under subgroups of the orthogonal group. Roughly speaking, we prove that if enough "mass" is concentrated around special orbits, then among the functions with prescribed symmetry, there is a solution for the original problem.;Our results can be regarded as a further development of the work of Z.-Q. Wang, where existence of local minima in the space of symmetric functions was studied for the Schrodinger equation. We illustrate the general theory with three examples, all of which produce new results. Our method allows the construction of solutions with prescribed symmetry, and it represents a step further in the classification of positive solutions for certain nonlinear elliptic problems.

机译：本文建立了具有亚临界和临界非线性的半线性椭圆型方程正解的存在性和多重性。我们在正交组的子组下对待不变的问题。粗略地说，我们证明了如果足够的“质量”集中在特殊轨道周围，那么在具有规定对称性的函数中，就有一个对原始问题的解决方案。;我们的结果可以看作是Z功的进一步发展。问Wang，针对Schrodinger方程研究了对称函数空间中局部极小值的存在。我们用三个例子来说明一般理论，所有例子都产生新的结果。我们的方法允许构造具有规定对称性的解，并且它代表对某些非线性椭圆问题的正解的分类中的又一步。

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作者
Catrina, Florin.;
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作者单位

Utah State University.;

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授予单位 Utah State University.;
学科 Mathematics.
学位 Ph.D.
年度 2000
页码 92 p.
总页数 92
原文格式 PDF
正文语种 eng
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专利

1. Radial symmetry and spherical nodal set of solutions of nonlinear elliptic equations. [J] . Seok Yong Jing Communications of the Korean Mathematical Society . 1995,第1期

机译：非线性椭圆型方程解的径向对称性和球面节点集。
2. Fowler transformation and radial solutions for quasilinear elliptic equations. Part 2: nonlinearities of mixed type [J] . Franca M Annali di matematica pura ed applicata . 2010,第1期

机译：拟线性椭圆型方程的Fowler变换和径向解。第2部分：混合类型的非线性
3. Fowler transformation and radial solutions for quasilinear elliptic equations. Part 2: nonlinearities of mixed type [J] . Matteo Franca Annali di Matematica Pura ed Applicata . 2010,第1期

机译：拟线性椭圆型方程的Fowler变换和径向解。第2部分：混合类型的非线性
4. Zhang dynamics with modified error-functions for online solution of nonlinear equations so as to avoid local minima [C] . Zhang Yunong, Ke Zhende, Li Kene, 2011 Chinese Control and Decision Conference . 2011

机译：带有修正误差函数的Zhang动力学用于非线性方程在线求解，以避免局部极小值
5. Existence and bifurcation of multiple positive solutions for some semilinear elliptic equations. [D] . Zhao, Xuejin. 1998

机译：一类半线性椭圆型方程的多个正解的存在性和分歧。
6. Spiraling elliptic Hermite-Gaussian solitons in nonlocal nonlinear media without anisotropy [O] . Guo Liang, Zhiping Dai -1

机译：无各向异性的非局域非线性介质中的椭圆椭圆厄米-高斯孤子的螺旋
7. Positive solutions of nonlinear elliptic equations―existence and nonexistence of solutions with radial symmetry in $Lsb{p}({f R}sp{N})$ [O] . J. F. Toland 1984

机译：非线性椭圆方程的正解 - $ l sb {p}（{ bf r} sp {n}）$

Positive solutions obtained as local minima via symmetries, for nonlinear elliptic equations.

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