4 papers
Quasilinear problems with critical Sobolev exponent for the Grushin p-Laplace operator
Somnath Gandal, Annunziata Loiudice, Jagmohan Tyagi
We study the following class of quasilinear degenerate elliptic equations with critical nonlinearity \begin{align*} \begin{cases}-Δ_{γ,p} u= λ|u|^{q-2}u+|u|^{p_γ^{*}-2}u & \text{ i…
Three non-zero solutions of a Neumann eigenvalue problems involving the fractional p-Laplacian
Somnath Gandal
In the present paper, we establish a multiplicity result for a following class of nonlocal Neumann eigenvalue problems involving the fractional p-Laplacian. \begin{align} \begin{ca…
Asymptotic behaviour of the least energy solutions of fractional semilinear Neumann problem
Somnath Gandal, Jagmohan Tyagi
We establish the asymptotic behaviour of the least energy solutions of the following nonlocal Neumann problem: \begin{align*} \left\{\begin{array}{l l} { d(-Δ)^{s}u+ u= \abs{u}^{p-…
The Neumann problem for a class of semilinear fractional equations with critical exponent
Somnath Gandal, Jagmohan Tyagi
We establish the existence of solutions to the following semilinear Neumann problem for fractional Laplacian and critical exponent: \begin{align*}\left\{\begin{array}{l l} { (-Δ)^{…