8 papers
Brezis-Nirenberg problems for mixed local-nonlocal operators with superlinear perturbations: compactness and applications
Mousomi Bhakta, Nirjan Biswas, Paramananda Das
In this paper, we consider the following mixed local nonlocal Brezis-Nirenberg problem \begin{equation}\label{crit_pro_abstract}\tag{} -Îu+(-Î)^s u=λ|u|^{p-2}…
Quasilinear problems with mixed local-nonlocal operator and concave-critical nonlinearities: Multiplicity of positive solutions
Mousomi Bhakta, Nirjan Biswas, Paramananda Das
We study the existence and multiplicity of positive solutions for the following concave-critical problem driven by an operator of mixed order obtained by the sum of the classical $…
Liouville results for supersolutions of fractional -Laplacian equations with gradient nonlinearities
Mousomi Bhakta, Anup Biswas, Aniket Sen
We prove that any nonnegative viscosity solution of the inequality must be constant. This r…
Liouville properties for differential inequalities with Laplacian operator
Mousomi Bhakta, Anup Biswas, Roberta Filippucci
In this paper, we establish several Liouville-type theorems for a class of nonhomogenenous quasilinear inequalities. In the first part, we prove various Liouville results associate…
Liouville results for -Laplacian elliptic equations with source terms involving gradient nonlinearities
Mousomi Bhakta, Anup Biswas, Roberta Filippucci
In this paper, we present a series of Liouville-type theorems for a class of nonhomogeneous quasilinear elliptic equations featuring reactions that depend on the solution and its g…
Critical -fractional problems involving a sandwich type nonlinearity
Mousomi Bhakta, Alessio Fiscella, Shilpa Gupta
In this paper, we deal with the following -fractional problem $$ (-Î)^{s_{1}}_{p}u +(-Î)^{s_{2}}_{q}u=λP(x)|u|^{k-2}u+θ|u|^{p_{s_{1}}^{*}-2}u \, \mbox{ in }\, Ω,\qquad…