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On unique solvability of a Dirichlet problem with nonlinearity depending on the derivative

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Języki publikacji
EN
Abstrakty
EN
In this work we consider second order Dirichelet boundary value problem with nonlinearity depending on the derivative. Using a global diffeomorphism theorem we propose a new variational approach leading to the existence and uniqueness result for such problems.
Rocznik
Strony
131--144
Opis fizyczny
Bibliogr. 17 poz.
Twórcy
  • Lodz University of Technology Institute of Mathematics Wólczańska 215, 90-924 Łódź, Poland
  • Lodz University of Technology Institute of Mathematics Wólczańska 215, 90-924 Łódź, Poland
Bibliografia
  • [1] G.A. Afrouzi, A. Hadjian, V.D. Radulescu, A variational approach of Sturm-Liouville problems with the nonlinearity depending on the derivative, Bound. Value Probl. 2015 (2015) 81.
  • [2] M. Bełdziński, M. Galewski, Global dijfeomorphism theorem applied to the solvability of discrete and continuous boundary value problems, J. Diff. Equ. Appl 24 (2018) 2, 277-290.
  • [3] D. Bors, A. Skowron, S. Walczak, System described by Volterra type integral operators, Dys. Cont. Dyn System B 19 (2014), 2401-2416.
  • [4] H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer, 2010.
  • [5] I. Ekeland, An inverse function theorem in Frechet spaces, Ann. Inst. Henri Poincare, Anal. Non Lineaire 28 (2011) 1, 91-105.
  • [6] D.G. Figueredo, Lectures on the Ekeland Variational Principle with Applications and Detours, Preliminary Lecture Notes, SISSA, 1988.
  • [7] D. Idczak, A global implicit function theorem and its applications to functional equations, Discrete Contin. Dyn. Syst., Ser. B 19 (2014) 8, 2549-2556.
  • [8] D. Idczak, On a generalization of a global implicit function theorem, Adv. Nonlinear Stud. 16 (2016) 1, 87-94.
  • [9] D. Idczak, A. Skowron, S. Walczak, On the diffeomorphisms between Banach and Hilbert spaces, Adv. Nonlinear Stud. 12 (2012) 1, 89-100.
  • [10] G. Katriel, Mountain pass theorems and global homeomorphism theorems, Ann. Inst. Henri Poincare, Anal. Non Lineaire 11 (1994) 2, 189-209.
  • [11] M. Majewski, Control system defined by some integral operator, Opuscula Math. 37 (2017) 2, 313-325.
  • [12] J. Mawhin, Problemes de Dirichlet Variationnels Non Lineaires, Seminaire de Mathe-matiques Superieures, vol. 104, Montreal, 1987.
  • [13] D. Motreanu, M. Tanaka, Multiple existence results of solutions for quasilinear elliptic equations with a nonlinearity depending on a parameter. Ann. Mat. Pura Appl. 193 (2014) 5, 1255-1282.
  • [14] M. Radulescu, S. Radulescu, Local inversion theorems without assuming continuous differentiability, J. Math. Anal. Appl. 138 (1989) 2, 581-590.
  • [15] B. Ricceri, A three critical points theorem revisited, Nonlinear Anal. 70 (2009), 3084-3089.
  • [16] C. Torres Ledesma, Existence of solutions for fractional Hamiltonian systems with nonlinear derivative dependence in R, J. Fract. Calc. Appl. 7 (2016) 2, 74-87.
  • [17] E. Zeidler, Applied Functional Analysis. Main Principles and Their Applications, Applied Mathematical Sciences, vol. 109, New York, Springer-Verlag, 1995.
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Bibliografia
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