CBMS Regional Conference in the Mathematical Sciences - "Finite Morse Index Solutions and Related Topics" -Winter 2007

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The lectures will involve boundary-value problems for nonlinear elliptic equations on bounded domains. They will encompass several important topics of current interest such as bifurcation theory, domain shape, Morse index solutions, and peak solutions; which occur in a great variety of applications of mathematics such as mathematical biology, catalysis theory, material science, and combustion. There will also be a discussion of interrelationships between these topics.The lectures will show a close connection between the theory of peak solutions and the theory of finite Morse index solutions. It is becoming increasingly apparent that finite Morse index solutions are very useful tools for studying nonlinear elliptic equations with rapid growth in the nonlinearity (faster than the critical growth). The talks will also include a number of interesting open problems that may be of interest to researchers in the area.