Pseudo-linear superposition principle for the Monge-Ampère equation based on generated pseudo-operations

Journal of Mathematical Analysis and Applications

Volumn 341, Issue 2, 2008, Pages 1427-1437

  Vivona, Doretta ^a   Štajner Papuga, Ivana ^b  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b UNIVERSITY OF NOVI SAD   (Serbia)

Author keywords

Monge Amp re equation; Pseudo operations; Pseudo superposition principle

Indexed keywords

EID: 39149102519     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2007.11.008     Document Type: Article

References (35)

1. Aczel J. Lectures on Functional Equations and Their Applications (1966), Academic Press, New York
2. Ampère A.M. Considérations générales sur les intégrales des équations aux différences partielles. J. École Polytech. 10 17 (1815) 549-611
3. Ames W.F. Ad hoc exact techniques for nonlinear partial differential equations. Nonlinear Partial Differential Equations in Engineering (1965), Academic Press, New York
4. Benvenuti P., and Mesiar R. Integrals with respect to a general fuzzy measure. In: Grabisch M., Murofushi T., and Sugeno M. (Eds). Fuzzy Measures and Integrals, Theory and Applications (2000), Physica-Verlag 205-232
5. Benvenuti P., Mesiar R., and Vivona D. Monotone set functions-based integrals. In: Pap E. (Ed). Handbook of Measure Theory, vol. II (2002), Elsevier, North-Holland 1329-1379
6. Bluman G.W., and Kumei S. Symmetries and Differential Equations (1989), Springer-Verlag, New York
7. Boillat G. Le champ scalaire de Monge-Ampère. K. Nor. Vidensk. Selsk. Forth. 41 (1968) 78-81
8. Boillat G. Sur l'équation générale de Monge-Ampère à plusieur variables. C. R. Math. Acad. Sci. Paris Ser. I 313 (1991) 805-808
9. Boillat G. Sur l'équation générale de Monge-Ampère d'ordre supérieur. C. R. Math. Acad. Sci. Paris Ser. I 315 (1992) 1211-1214
10. Donato A., Ramgulam U., and Rogers C. The (3 + 1)-dimensional Monge-Ampère equation in discontinuity were theory: Application of a reciprocal transformation. Meccanica 27 (1992) 257-262
11. Goard J.M., and Broadbridge P. Nonlinear superposition principles obtained lie symmetry methods. J. Math. Anal. Appl. 214 (1997) 633-657
12. Grabisch M., Nguyen H.T., and Walker E.A. Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference (1995), Kluwer Academic Publishers, Dordrecht
13. Inselberg A. Noncommutative superpositions for nonlinear operators. J. Math. Anal. Appl. 29 (1970) 294-298
14. Jones S.E., and Ames W.F. Nonlinear superposition. J. Math. Anal. Appl. 17 (1967) 484-487
15. Klement E.P., Mesiar R., and Pap E. Triangular Norms (2000), Kluwer Academic Publishers, Dordrecht
16. Kolokoltsov V.N., and Maslov V.P. Idempotent Analysis and Its Applications (1997), Kluwer Academic Publishers, Dordrecht
17. Levin S.A. Principles of nonlinear superposition. J. Math. Anal. Appl. 30 (1970) 197-205
18. Marková-Stupňanová A. A note on g-derivative and g-integral. Tatra Mt. Math. Publ. 8 (1996) 71-76
19. Maslov V.P., and Samborskij S.N. Idempotent analysis. In: Maslov V.P., and Samborskij S.N. (Eds). Advances in Soviet Mathematics, vol. 13 (1992), Amer. Math. Soc., Providence
20. Mesiar R. Pseudo-linear integrals and derivatives based on a generator g. Tatra Mt. Math. Publ. 8 (1996) 67-70
21. Oliveri F. Linearizable second order Monge-Ampère equation. J. Math. Anal. Appl. 218 (1998) 329-345
22. Oliveri F. Lie group analysis of differential equations: Direct and inverse problems. Note Mat. 23 (2004) 195-216
23. Oliveri F. Sur une Propriété Remarquable des Équations de Monge-Ampère. Rend. Circ. Mat. Palermo (2) Suppl. 78 (2006) 243-258
24. Pap E. g-Calculus. Univ. Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 23 1 (1993) 145-156
25. Pap E. Null-Additive Set Functions (1995), Kluwer Academic Publishers, Dordrecht
26. Pap E. Solving nonlinear equations by nonadditive measures. Nonlinear Anal. 30 (1997) 31-40
27. Pap E. Pseudo-additive measures and their applications. In: Pap E. (Ed). Handbook of Measure Theory, vol. II (2002), Elsevier, North-Holland 1403-1465
28. Pap E. Applications of the generated pseudo-analysis to nonlinear partial differential equations. Contemp. Math. 377 (2005) 239-259
29. Pap E., and Ralević N. Pseudo operations on finite intervals. Novi Sad J. Math. 29 1 (1999) 9-18
30. Pap E., and Štajner I. Generalized pseudo-convolution in the theory of probabilistic metric spaces, information, fuzzy numbers, optimization, system theory. Fuzzy Sets and Systems 102 (1999) 393-415
31. Pap E., and Vivona D. Non-commutative and non-associative pseudo-analysis and its applications on nonlinear partial differential equations. J. Math. Anal. Appl. 246 2 (2000) 390-408
32. Pap E., Vivona D., and Štajner-Papuga I. On a pair of generated pseudo-operations with three parameters and its application on the Burger's type equations. Atti Sem. Mat. Fis. Univ. Modena L (2002) 451-464
33. Sprijker M.N. Superposition in linear and nonlinear ordinary differential equations. J. Math. Anal. Appl. 30 (1970) 206-222
34. Ruggeri T. Su una naturale estensione a tre variabili dell'equazione di Monge-Ampère. Rend. Accad. Naz. Lincei 55 (1973) 445-449
35. Wang Z., and Klir G.J. Fuzzy Measure Theory (1992), Plenum Press, New York