Existence and uniqueness of solutions to distributional differential equations involving Henstock–Kurzweil–Stieltjes integrals

• Autores: GUOJU YE, Mingxia Zhang, Wei Liu, Dafang Zhao
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 60, Nº. 2, 2019, págs. 443-458
• Idioma: inglés
• DOI: 10.33044/revuma.v60n2a11
• Enlaces
  • Texto completo (pdf)
• Resumen

  • This paper is concerned with the existence and uniqueness of solutions to the second order distributional differential equation with Neumann boundary value problem via Henstock–Kurzweil–Stieltjes integrals.The existence of solutions is derived from Schauder’s fixed point theorem, and the uniqueness of solutions is established by Banach’s contraction principle. Finally, two examples are given to demonstrate the main results.

• Referencias bibliográficas
  • A. Ca˜nada, J.A. Montero, S. Villegas, Liapunov-type inequalities and Neumann boundary value problems at resonance. Math. Inequal. Appl. 8...
  • P.C. Das, R.R. Sharma, Existence and stability of measure differential equations. Czechoslovak Math. J. 22(97) (1972), 145–158. MR 0304815.
  • D. Fraˇnkov´a, Regulated functions. Math. Bohem. 116 (1991), no. 1, 20–59. MR 1100424.
  • G.H. Hardy, Weierstrass’s non-differentiable function. Trans. Amer. Math. Soc. 17 (1916), no. 3, 301–325. MR 1501044.
  • P. Krejˇc´ı, P. Lauren¸cot, Generalized variational inequalities. J. Convex Anal. 9 (2002), no. 1, 159–183. MR 1917394.
  • P.Y. Lee, Lanzhou Lectures on Henstock Integration. World Scientific, Singapore, 1989. MR 1050957.
  • G.A. Monteiro, A. Slav´ık, M. Tvrd´y, Kurzweil–Stieltjes Integral. World Scientific, Singapore, 2019. MR 3839599.
  • G.A. Monteiro, B. Satco, Distributional, differential and integral problems: equivalence and existence results. Electron. J. Qual. Theory...
  • S. S´anchez-Perales, J. F. Tenorio, Laplace transform using the Henstock–Kurzweil integral. Rev. Un. Mat. Argentina 55 (2014), no. 1, 71–81....
  • S. S´anchez-Perales, The initial value problem for the Schr¨odinger equation involving the Henstock–Kurzweil integral. Rev. Un. Mat. Argentina...
  • B. Satco, Regulated solutions for nonlinear measure driven equations. Nonlinear Anal. Hybrid Syst. 13 (2014), 22–31. MR 3209695.
  • S. Schwabik, G. J. Ye, Topics in Banach space Integration. World Scientific, Singapore, 2005. ˇ MR 2167754.
  • J.P. Sun, W.T. Li, Multiple positive solutions to second-order Neumann boundary value problems. Appl. Math. Comput. 146 (2003), no. 1, 187–194....
  • E. Talvila, The regulated primitive integral. Illinois J. Math. 53 (2009), no. 4, 1187-1219. MR 2741185