Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales
ISSN 0370-3908
COSSIO, Jorge. Existence and multiplicity of solutions to semilinear and quasilinear elliptic problems. []. , 39, 151, pp.138-151. ISSN 0370-3908. https://doi.org/10.18257/raccefyn.193.
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.
: Semilinear elliptic equations; quasilinear elliptic equations; variational methods; Lyapunov-Schmidt reduction; Leray-Schauder degree; Morse theory; bifurcation theory.