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Existence of solutions for a nonlinear problem at resonance

Haddaoui Mustapha, Lebrimchi Hafid, Ouhamou Brahim, Tsouli Najib

Demonstratio Mathematica

2022

Vol. 55, nr 1

482--489

In this work, we are interested at the existence of nontrivial solutions for a nonlinear elliptic problem with resonance part and nonlinear boundary conditions. Our approach is variational and is based on the well-known Landesman-Laser-type conditions.

Nonlinear boundary condition in electromagnetic theory - analytical scheme of formulation

Sowa M., Spałek D.

Archives of Electrical Engineering

2013

Vol. 62, nr 1

163-177

The paper presents a method of how the nonlinear boundary condition [1] may be applied in nonlinear problems of electromagnetic field theory. It is introduced for problems with nonlinear conductivity. An analytical procedure has been constructed, which seeks to reduce calculations related with the nonlinear region. In order to verify the proposed solutions, two problems have been formulated: one of linear and the other of cylindrical symmetry. These have been additionally solved by the authors’ modification of the perturbation method that has been described in previous papers [7, 8, 10]. The electromagnetic field distribution obtained thereby has served as a referential result since it can obtain very accurate solutions [10]. Relative errors of electric and magnetic field strength are introduced to verify the results.

On the nonexistence of positive solution of Laplace equation in half-space Rn with a nonlinear Neumann boundary condition

Binh D. T. T., Long N. T.

Demonstratio Mathematica

2000

Vol. 33, nr 2

365-372

On nonexistence of positive solution of a nonlinear Neumann problem in half-space Rn+

Binh D., Diem T., Ruy D., Long T.

Demonstratio Mathematica

1998

Vol. 31, nr 4

773-782