Abstract
In this paper I present some results of my research studying existence, multiplicity, and qualitative properties of solutions to semilinear elliptic problems of the type and to quasilinear elliptic problems of the type where D is the Laplace operator, Dp is the p-Laplacian, W ⊂ RN (N ≥ 2) is a bounded domain in RN with smooth boundary, and f : R → R is a nonlinear function. Our theorems were obtained by using variational methods, a minmax principlie developed in Castro, Cossio & Neuberger (1997), Leray-Schauder degree, Morse theory, and bifurcation theory. Besides statement of principal results, we present some open problems which seem of interest for nonlinear analysts.
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