Dergiler / Hacettepe Journal of Mathematics and Statistics / 2008 / Cilt: 37 - Sayı: 1

On semi-continuous mappings, equations and inclusions in a Banach space

Sayfa
9–24
Yayın Tarihi
2022-10-18
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

In particular, a solvabil- ity theorem of the mixed problem for a nonlinear hyperbolic equation is proved, and one Nirenberg problem is studied.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:We investigate the description of the image of a continuous mappings acting in a Banach space, and the solvability of equations and inclu- sions.
📊
Temel Bulgular & Veri:The results obtained can be applied to the Cauchy problem for a nonlinear differential equation (or inclusion).
💡
Sonuç & Katkı:In particular, a solvabil- ity theorem of the mixed problem for a nonlinear hyperbolic equation is proved, and one Nirenberg problem is studied.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

We investigate the description of the image of a continuous mappings acting in a Banach space, and the solvability of equations and inclu- sions. The results obtained can be applied to the Cauchy problem for a nonlinear differential equation (or inclusion). In particular, a solvabil- ity theorem of the mixed problem for a nonlinear hyperbolic equation is proved, and one Nirenberg problem is studied.

🔖

Bu Makaleye Atıf Yap

SOLTANOV, K. N. (2022). On semi-continuous mappings, equations and inclusions in a Banach space. Hacettepe Journal of Mathematics and Statistics, Cilt: 37 - Sayı: 1, 9–24. https://ajindex.com/articles/530714

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (19)

  1. Akagi, G. and ˆOtani, M. Evolution inclusions governed by the difference of two subdiffer- entials in reflexive Banach spaces, J. Diff. Equ. 209 (2), 397–415, 2005
  2. Amann, H. and Quittner, P. Semilinear parabolic equations involving measures and low regularity data, Trans. Amer. Math. Soc. 356, 1045–1119, 2004
  3. Aubin, J. -P. and Ekeland, I. Applied nonlinear analysis (Willey, 1984)
  4. Barbu, V., Lasiecka, I. and Rammaha, M.A. On nonlinear wave equations with degenerate damping and source terms, Trans. Amer. Math. Soc. 357, 2571–2611, 2005
  5. Browder, F.E. and Petryshyn, W.V. Approximation methods and the generalized topological degree for nonlinear mappings in Banach spaces, J. Functional Analysis 3 (2), 217–245, 1969
  6. Deville, R., Godefroy, G. and Zizler, V. Smoothness and renorming in Banach spaces (Long- man Sci. & Tech., 1993)
  7. Diestel, J. Geometry of Banach spaces. Selected Topics (Lecture Notes in Math., Springer Verlag 485, 1975)
  8. Dunford, N. and Schwartz, J.T. Linear Operators. Pt. 1: General Theory (Willey, 1967)
  9. Eells, J. Jr. A setting for global analysis, Bull. Amer. Math. Soc. 72, 751–807, 1966
  10. Hu Sh., Lakshmikantham, V. and Papageorgiou, N. S. On the properties of the solution set of semilinear evolution inclusions, Nonlinear Analysis 24 (12), 1683–1712, 1995
  11. Hu Sze-Tsen Homotopy theory (Acad. Press, New-York & London, 1959)
  12. Klee V.L. - (a) Convex bodies and periodic homeomorphisms in Hilbert space. (1953) Trans. AMS, 74; (b) Some topological properties of convex sets. (1955) Trans. AMS, 78, 30-55
  13. Ladas, G.E. and Lakshmikantham, V. Differential equations in abstract spaces (Acad. Press, New York-London, 1976)
  14. Levine, H. Instability and nonexistence of global solutions to nonlinear wave equations of the form Putt = −Au + F (u), Trans. AMS 192, 1–21, 1974
  15. Lions, J. -L. Quelques methodes de resolution des problemes aux limites non lineares (DUNOD, Gauthier-Villars, Paris, 1969)
  16. Lions, J. -L. and Magenes, E. Non-homogeneous boundary value problems and applications (v.I) (Springer-Verlag, Berlin-He´ydelberg-New York, 1972)
  17. Michael, E.A. Continuous selections - I, Ann. Math. 63 (2), 361–381, 1956
  18. Pohozaev, S. I. On nonlinear operators which have a weakly closed images and quasilinear elliptic equations (Russian) Mat. Sb. (N.S.) 78 (120), 237–259, 1969
  19. Soltanov, K.N. Nonlinear mappings and the solvability of nonlinear equations. Soveit. Math. Dokl. 34 (1), 24