Multiple nontrivial solutions for semilinear elliptic problems

We study the existence of multiple constant sign and nodal (sign-changing) solutions for semilinear elliptic equations. Our approach is based on a combination of variational techniques using critical point theory, of the method of upper-lower solutions and of Morse theory (critical groups). We prove several multiplicity results. Our analytical framework incorporates both coercive and superlinear parametric problems.