Multiple solutions for a coercive quasilinear elliptic equation via Morse theory

We study the quasilinear elliptic problem which is resonant at zero. By using Morse theory, we obtain five nontrivial solutions for the equation with coercive nonlinearities.

Existence Results for a Class of the Quasilinear Elliptic Equations with the Logarithmic Nonlinearity

In this paper, the nonlinear quasilinear elliptic problem with the logarithmic nonlinearity − div ∇ u p − 2 ∇ u = a x φ p u log u + h x ψ p u in Ω ⊂ R n was studied. By means of a double perturbation argument and Nehari manifold, the authors obtain the existence results.