Author

Kanishka Perera

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Open access Sep 2026

Critical quasilinear elliptic systems with convex subcritical perturbations

We study a class of Dirichlet problems for coupled quasilinear elliptic systems driven by the p–Laplacian in a bounded domain, where the nonlinear terms split into a critical homogeneous part and a convex subcritical perturbation. Using variational methods, a nonlinear eigenvalue theory based on the Fadell–Rabinowitz Z...

Elisandra Gloss, Bruno Ribeiro, Artur Jorge Marinho et al. · Calculus of Variations and P... · 0 citations

Preprint Sep 2026

Doubly critical mixed-order quasilinear equations: existence, multiplicity and regularity

We investigate a class of mixed-order quasilinear elliptic equations in $\mathbb R^N$ driven by the $q$-biharmonic and $p$-Laplacian operators, \[ \Delta_q^2u-\Delta_pu = \lambda\frac{|u|^{r_\sigma-2}u}{|x|^\sigma} +|u|^{p^*-2}u +|u|^{q^{**}-2}u, \] where $1<q<N/2$, $1<p<q^*$, $p\ne q$, $q\ne p^*$, and th...

Elisandra Gloss, Artur Jorge Marinho, Kanishka Perera et al. · 0 citations

Preprint Aug 2026

On biharmonic equations with $p$-Laplacian and indefinite potentials or critical nonlinearity

In this paper we consider nonlinear biharmonic equations with $p$-Laplacian ($p\ge2$) of the form $$ \left\{ \begin{array}{l} \Delta^2 u - \Delta_p u + V (x) u = f (x, u) \text{,} u \in H^2 (\mathbb{R}^N) \text{,} \end{array} \right. $$ where the potential $V(x)$ may be indefinite. Using local linking and Morse theory,...

Shi-Bo Liu, Kanishka Perera · 0 citations