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Mathematical modeling of semiconductor quantum dots based on the nonparabolic effective-mass approximation

Jinn-Liang Liu (2012)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

Within the effective mass and nonparabolic band theory, a general framework of mathematical models and numerical methods is developed for theoretical studies of semiconductor quantum dots. It includes single-electron models and many-electron models of Hartree-Fock, configuration interaction, and current-spin density functional theory approaches. These models result in nonlinear eigenvalue problems from a suitable discretization. Cubic and quintic Jacobi-Davidson methods of block or nonblock version...

Multiple positive solutions for quasilinear elliptic problems with sign-changing nonlinearities.

Fernández Bonder, Julián (2004)

Abstract and Applied Analysis

Multiple radially symmetric solutions for a quasilinear eigenvalue problem.

Mezei, Ildikó-Ilona (2009)

Acta Universitatis Sapientiae. Mathematica

Multiple solutions for nonlinear discontinuous elliptic problems near resonance

Nikolaos Kourogenis, Nikolaos Papageorgiou (1999)

Colloquium Mathematicae

We consider a quasilinear elliptic eigenvalue problem with a discontinuous right hand side. To be able to have an existence theory, we pass to a multivalued problem (elliptic inclusion). Using a variational approach based on the critical point theory for locally Lipschitz functions, we show that we have at least three nontrivial solutions when $λ \to λ_{1}$ from the left, $λ_{1}$ being the principal eigenvalue of the p-Laplacian with the Dirichlet boundary conditions.

Multiple solutions for the $p$ -Laplace equation with nonlinear boundary conditions.

Bonder, Julián Fernández (2006)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Multiplicity of symmetric solutions for a nonlinear eigenvalue problem in $ℝ^{n}$ .

Visetti, Daniela (2005)