10 papers
Nonlinear elliptic Dirichlet boundary value problems on time scales
Shalmali Bandyopadhyay, F. Ayça Çetinkaya, Tom Cuchta
We establish existence and uniqueness results for nonlinear elliptic Dirichlet boundary value problems on n-dimensional time scale domains. Time scales provide a unified framework…
Positive solutions of elliptic systems with superlinear nonlinearities on the boundary
Shalmali Bandyopadhyay, Maya Chhetri, Briceyda Delgado +2
We consider elliptic systems with superlinear and subcritical boundary conditions and a bifurcation parameter as a multiplicative factor. By combining the rescaling method with deg…
Existence results for quasimonotone elliptic systems with growth up to critical exponents
Shalmali Bandyopadhyay, Briceyda B. Delgado, Nsoki Mavinga +1
We establish the existence of weak solutions of coupled systems of elliptic partial differential equations with quasimonotone nonlinearities in the differential equation and on the…
Numerical Approximation and Bifurcation Results for an Elliptic Problem with Superlinear Subcritical Nonlinearity on the Boundary
Shalmali Bandyopadhyay, Thomas Lewis, Dustin Nichols
We develop numerical algorithms to approximate positive solutions of elliptic boundary value problems with superlinear subcritical nonlinearity on the boundary of the form $-Δu + u…
Prüfer Transformation and Spectral Analysis for a Sturm--Liouville-Type Equation
Shalmali Bandyopadhyay, F. Ayça Çetinkaya, Tom Cuchta
We study a second-order differential equation involving a quasi-derivative, leading to a non-self-adjoint Sturm--Liouville-type problem with four coefficient functions. To analyze…
Existence Result for Difference Equations on Non-Uniform Grids via Upper and Lower Solution Method
Shalmali Bandyopadhyay, Kimser Lor
This paper establishes an existence theory for discrete second-order boundary value problems on non-uniform time grids using the upper and lower solution method. We consider differ…