<abstract xmlns="http://www.w3.org/1999/xhtml"> In this paper, we study the existence of positive solutions for the following nonlinear polyharmonic equation (-∆)mu+λf(x, u) = 0 in B; subject to some boundary conditions, where m is a positive integer, λ is a nonnegative constant and B is the unit ball of ℝn (n ≥ 2). Under some appropriate assumptions on the nonnegative nonlinearity term f(x, u) and by using the Schäuder fixed point theorem, the existence of positive solutions is obtained. At last, examples are given for illustration. </abstract>

In this paper, we study the existence of positive solutions for the following nonlinear polyharmonic equation (-∆)mu+λf(x, u) = 0 in B; subject to some boundary conditions, where m is a positive integer, λ is a nonnegative constant and B is the unit ball of ℝn (n ≥ 2). Under some appropriate assumptions on the nonnegative nonlinearity term f(x, u) and by using the Schäuder fixed point theorem, the existence of positive solutions is obtained. At last, examples are given for illustration.

Positive bounded solutions for nonlinear polyharmonic problems in the unit ball

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Positive bounded solutions for nonlinear polyharmonic problems in the unit ball"}

In this paper, we study the existence of positive solutions for the following nonlinear polyharmonic equation (-∆)mu+λf(x, u) = 0 in B; subject to some...

Positive bounded solutions for nonlinear polyharmonic problems in the unit ball

Published Online: Mar 31, 2018

Page range: 143 - 153

Received: Jul 29, 2016

Accepted: Mar 06, 2017

DOI: https://doi.org/10.1515/auom-2017-0041

Keywords
Green function, Kato class, Positive solution, Nonlinear polyharmonic equation, Schäuder fixed point theorem

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Positive bounded solutions for nonlinear polyharmonic problems in the unit ball

Published Online: Mar 31, 2018

Page range: 143 - 153

Received: Jul 29, 2016

Accepted: Mar 06, 2017

DOI: https://doi.org/10.1515/auom-2017-0041

KeywordsGreen function, Kato class, Positive solution, Nonlinear polyharmonic equation, Schäuder fixed point theorem

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Green function, Kato class, Positive solution, Nonlinear polyharmonic equation, Schäuder fixed point theorem