K. Perera

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math.AP2025

Nonlocal Dirichlet problems involving the Logarithmic $p$ -Laplacian

Rakesh Arora, Hichem Hajaiej, Kanishka Perera

In this work, we show the existence of an unbounded sequence of minimax eigenvalues for the logarithmic $p$ -Laplacian via the $Z_{2}$ -cohomological index of Fadell and Rabin…

math.AP2025

Critical p-biharmonic problems and applications to Hamiltonian systems

Kanishka Perera, Bruno Ribeiro

We study fourth-order quasilinear elliptic problems that involve the p-biharmonic operator and Navier boundary conditions. The nonlinear term grows at the critical Sobolev rate. St…

math.AP2025

Nonlocal critical elliptic equations in homogeneous fractional Sobolev spaces

Siegfried Carl, Kanishka Perera, Hossein Tehrani

We prove new multiplicity results for some nonlocal critical growth elliptic equations in homogeneous fractional Sobolev spaces. The proofs are based on an abstract critical point…

math.AP2025

Global $L^{\infty}$ and decay estimate for fractional $p$ -Laplacian equations in $D^{s, p} (R^{N})$

Siegfried Carl, Kanishka Perera, Hossein Tehrani

In this paper we present a new global $L^{\infty}$ -estimate for solutions $u \in D^{s, p} (R^{N})$ of the fractional $p$ -Laplacian equation % $$ u\in D^{s,p}(\R^N): (-Î_p)^s u=f(x,u) \q…

math.AP2024

A bifurcation and multiplicity result for a critical growth elliptic problem

Said El Manouni, Kanishka Perera

We consider a BrÃ©zis-Nirenberg type critical growth $p$ -Laplacian problem involving a parameter $I^¼ > 0$ in a smooth bounded domain $I^c ◯$ . We prove the existence of multiple nontriv…

math.AP2024

Abstract multiplicity theorems and applications to critical growth problems

Kanishka Perera

We prove some abstract multiplicity theorems that can be used to obtain multiple nontrivial solutions of critical growth $p$ -Laplacian and $(p, q)$ -Laplacian type problems. We show…

Nonlocal Dirichlet problems involving the Logarithmic p-Laplacian

Critical p-biharmonic problems and applications to Hamiltonian systems

Nonlocal critical elliptic equations in homogeneous fractional Sobolev spaces

Global L∞ and decay estimate for fractional p-Laplacian equations in Ds,p(RN)

A bifurcation and multiplicity result for a critical growth elliptic problem

Abstract multiplicity theorems and applications to critical growth problems

Nonlocal Dirichlet problems involving the Logarithmic $p$ -Laplacian

Global $L^{\infty}$ and decay estimate for fractional $p$ -Laplacian equations in $D^{s, p} (R^{N})$