Nodal and multiple solutions for nonlinear periodic problems with competing nonlinearities (Q2853988)

The authors consider a nonlinear periodic problem on \(\mathbb{R}^1\) driven by a nonhomogeneous differential operator which incorporates as a special case the scalar \(p\)-Laplacian, and a reaction which exhibits the competition of concave and convex terms. Using variational methods based on critical point theory, together with suitable truncation techniques and Morse theory (critical groups), they establish the existence of five nontrivial solutions, two positive, two negative and the fifth nodal (sign-changing).