Document Type
Thesis
Date of Award
5-31-1987
Degree Name
Master of Science in Applied Mathematics - (M.S.)
Department
Mathematics
First Advisor
Petronije Milojevic
Second Advisor
John Tavantzis
Third Advisor
Denis L. Blackmore
Abstract
This thesis consists of two parts. In the first part, Chapters I and II, we present some basic critical point theory,for functionals bounded from below on some Banach space and are either weakly lower semicontinuous or satisfy the Palais-Smale compactness condition. Moreover, we also prove some Mountain Pass type theorems of Ambrosetti and Rabinowit for functionals which are neither bounded from below nor above. In the second part, Chapters III - V, we apply these Mountain Pass type results to the problems of the existence of positive solutions for nonlinear elliptic equations of the Δu = up + f(x,u) , where u > 0 on Ω , u = 0 on aΩ. , and the problems of nontrivial solutions for equations of the form (||)-Δu=|u|p-1u + f(x,u) , where u = 0 on Ω , u = 0 on aΩ, and Rn is a bounded domain, n > 3, 1 < p < (n+2)/(n-2) and f(x,u)/up → 0 as u → ∞. When p = (n+2)/(n-2), we prove in detail the basic results of Brezis-Nirenberg for (I) and of Capozzi-Fortunato-Palmieri for (II) using the dual variational method.
Recommended Citation
Wu, Hwei-Ling, "Variational theory and applications to nonlinear elliptic equations involving critical Sobolev exponents" (1987). Theses. 3337.
https://digitalcommons.njit.edu/theses/3337
