Document Type : Research Paper

Authors

• Svetlin Georgiev ¹
• Khaled Zennir ²

¹ Department of Differential Equations, Faculty of Mathematics and Informatics, University of Sofia, Sofia, Bulgaria

² Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass, Saudi Arabia

Abstract

The purpose of studying the discipline of nonlinear wave processes is to knowledge of the current state of nonlinear wave problems in mechanics and an understanding of its main problems, as well as to develop general skills for solving these problems using new methods of mathematical. We consider a class of initial boundary value problems for one-dimensional nonlinear wave processes. A new topological approach is applied to prove the existence of at least two nonnegative classical solutions.  The arguments are based on a recent theoretical result.

Keywords

• Partial differential equations
• Existence results
• Green function
• Nonlinear hyperbolic processes
• Positive solution
• Fixed point
• Cone
• Sum of operators
• Nonnegative classical solutions