Volume 7, Issue 5
Existence, Asymptotics and Computation of Solutions of Nonlinear Sturm-Liouville Problems

Noureddine Frimane

J. Nonl. Mod. Anal., 7 (2025), pp. 1811-1829.

Published online: 2025-09

[An open-access article; the PDF is free to any online user.]

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  • Abstract

This paper deals with the existence, asymptotics and computation of solutions of nonlinear Sturm-Liouville problems with general separated boundary conditions. The approach centers first on converting these problems into Hammerstein integral equations with modified argument, and then applying the Banach and Rothe fixed point theorems to solve them. This approach not only enabled us to prove existence theorems for these problems, but also to derive general and accurate asymptotic formulae for their solutions. Finally, an illustrative numerical example is presented using the Picard’s iteration method.

  • AMS Subject Headings

34B15, 34B24, 34L16, 34L20, 47H30

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COPYRIGHT: © Global Science Press

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@Article{JNMA-7-1811, author = {Frimane , Noureddine}, title = {Existence, Asymptotics and Computation of Solutions of Nonlinear Sturm-Liouville Problems}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2025}, volume = {7}, number = {5}, pages = {1811--1829}, abstract = {

This paper deals with the existence, asymptotics and computation of solutions of nonlinear Sturm-Liouville problems with general separated boundary conditions. The approach centers first on converting these problems into Hammerstein integral equations with modified argument, and then applying the Banach and Rothe fixed point theorems to solve them. This approach not only enabled us to prove existence theorems for these problems, but also to derive general and accurate asymptotic formulae for their solutions. Finally, an illustrative numerical example is presented using the Picard’s iteration method.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2025.1811}, url = {http://global-sci.org/intro/article_detail/jnma/24391.html} }
TY - JOUR T1 - Existence, Asymptotics and Computation of Solutions of Nonlinear Sturm-Liouville Problems AU - Frimane , Noureddine JO - Journal of Nonlinear Modeling and Analysis VL - 5 SP - 1811 EP - 1829 PY - 2025 DA - 2025/09 SN - 7 DO - http://doi.org/10.12150/jnma.2025.1811 UR - https://global-sci.org/intro/article_detail/jnma/24391.html KW - Approximate methods, asymptotic expansion, Jacobi elliptic functions, ordinary differential equation, nonlinear eigenvalue problem. AB -

This paper deals with the existence, asymptotics and computation of solutions of nonlinear Sturm-Liouville problems with general separated boundary conditions. The approach centers first on converting these problems into Hammerstein integral equations with modified argument, and then applying the Banach and Rothe fixed point theorems to solve them. This approach not only enabled us to prove existence theorems for these problems, but also to derive general and accurate asymptotic formulae for their solutions. Finally, an illustrative numerical example is presented using the Picard’s iteration method.

Frimane , Noureddine. (2025). Existence, Asymptotics and Computation of Solutions of Nonlinear Sturm-Liouville Problems. Journal of Nonlinear Modeling and Analysis. 7 (5). 1811-1829. doi:10.12150/jnma.2025.1811
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