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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.

Newton's iteration with a conjugate gradient based decomposition method for an elliptic PDE with a nonlinear boundary condition

Koko J.

International Journal of Applied Mathematics and Computer Science

2004

Vol. 14, no 1

13-18

Newton's iteration is studied for the numerical solution of an elliptic PDE with nonlinear boundary conditions. At each iteration of Newton's method, a conjugate gradient based decomposition method is applied to the matrix of the linearized system. The decomposition is such that all the remaining linear systems have the same constant matrix. Numerical results confirm the savings with respect to the computational cost, compared with the classical Newton method with factorization at each step.