We consider a nonlinear elliptic equation driven by the $p$-Laplacian with Dirichlet boundary condition. Using variational techniques, combined with the method of upper-lower solutions and suitable truncation arguments, we establish the existence of at least six nontrivial solutions: two positive, two negative and two nodal (sign-changing) solutions. Our framework of analysis incorporates both coercive and $p-1$-superlinear problems. Also, the result on multiple constant sign solution incorporates the case of concave-convex nonlinearities.
"A unified approach for multiple constant sign and nodal solutions." Adv. Differential Equations 12 (12) 1363 - 1392, 2007. https://doi.org/10.57262/ade/1355867406