| International Journal of Nonlinear Analysis and Applications | ||
| Article 250, Volume 13, Issue 1, January 0, Pages 3093-3101 PDF (397.69 K) | ||
| DOI: 10.22075/ijnaa.2021.23609.2565 | ||
| Receive Date: 06 June 2021, Revise Date: 25 August 2021, Accept Date: 04 September 2021 | ||
| References | ||
|
[1] J. Bourgain, Global solutions of nonlinear Schr¨odinger equations, AMS, Colloquium Publications, vol. 46, 1999. [2] J.F. Colombeau, Elementary Introduction in New Generalized Functions, North Holland, Amsterdam, 1985. [3] J.F. Colombeau, New Generalized Function and Multiplication of Distribution, North Holland, Amsterdam /New York / Oxford, 1984. [4] R. Hermann and M. Oberguggenberger, Ordinary Differential Equations and Generalized Functions, M. Grosser, G. H¨ormann, M.Kunzinger, M. Oberguggenberger (Eds.), Proc. Workshop: Nonlinear Theory of Generalized Functions, E.Schrodinger Inst, Vienna, October-December 1997, in: Research Notes in Mathematical Series, Chapman and Hall/CRC, 1999. [5] D. Rajterc Ciric and M. Stojanovic, Convolution-type derivatives and transforms of Colombeau generalized stochastic processes, Integral Transforms Spec. Funct. 22(45) (2011) 319–326. [6] M. Reed and B. Simon, Methods of Modern Mathematical Physics, II: Fourier Analysis, Self-Adjointness, Academic Press, NewYork, 1975. [7] M. Stojanovic, Extension of Colombeau algebra to derivatives of arbitrary order Dα, α ∈ R+ ∪ {0}. Application to ODEs and PDEs with entire and fractional derivatives, Nonlinear Anal. 71(11) (2009) 5458–5475. [8] M. Stojanovic, Fondation of the fractional calculus in generalized function algebras, Anal. Appl. 10(4) (2012) 439–467. [9] M. Stojanovic, Nonlinear Schr¨odinger equation with singular potential and initial data, Nonlinear Anal. 64 (2006) 1460–1474. [10] S. Nakamura, Lectures on Schr¨odinger Operators, Lectures given at the University of Tokyo, October 1992, February 1993. [11] M. Oberguggenberger, Generalized functions in nonlinear models a survey, Nonlinear Anal. 47 (2001) 5049–5040. [12] C.L. Zhi and B. Fisher, Several products of distributions on Rm, Proc. R. Soc. Lond. A 426 (1989) 425–439. | ||
|
Statistics Article View: 16,152 PDF Download: 9,615 |
||