2011/01/10 by F. Güngör, Güngör, Faruk, Mahir Hasanov +1
Computer Science · Mathematics · #35D05 #35J60 #35p15 #47A75 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Primary 49R50 #Secondary 34L15 #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1101.1827
openalex publication_date 2011/01/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
This paper is devoted to multi-parameter eigenvalue problems for perturbed p-Laplacians, modelling travelling waves for a class of non-linear evolution PDE. Dispersion relations between the eigen-para-meters, the existence of eigenvectors and positive eigenvectors, variational principles for eigenvalues of perturbed p-Laplacians and constructing analytical solutions are the main subject of this paper. Besides the p-Laplacian-like eigenvalue problems we also deal with new and non-standard eigenvalue problems, which can not be solved by the methods used in nonlinear eigenvalue problems for p-Laplacians and similar operators. We do both: extend and use classical variational and analytical techniques to solve standard eigenvalue problems and suggest new variational and analytical methods to solve the non-standard eigenvalue problems we encounter in the search for travelling waves.