On a Parametric Nonlinear Dirichlet Problem with Subdiffusive and Equidiffusive Reaction

We study a nonlinear parametric elliptic equation (nonlinear eigenvalue problem) driven by a nonhomogeneous differential operator. Our setting incorporates equations driven by the p-Laplacian, the (p, q)-Laplacian, and the generalized p-mean curvature differential operator. Applying variational methods we show that for lambda > 0 (the parameter) sufficiently large the problem has at least three nontrivial smooth solutions whereby one is positive, one is negative and the last one has changing sign ( nodal). In the particular case of (p, 2)-equations, using Morse theory, we produce another nodal solution for a total of four nontrivial smooth solutions.