ON ESTIMATIONS IN AN EQUATION WITH A PARAMETER AND A DISCONTINUOUS OPERATOR

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Resumo

In a real reflexive Banach space, an equation with a parameter and a discontinuous nonlinear operator is considered. Both parameter estimations and operator norms are found for the equation. These estimations validate and define concretely the similar estimations obtained earlier in problems with a parameter for elliptic and ordinary differential equations with discontinuous right-hand sides.

Sobre autores

D. Potapov

Saint Petersburg State University

Email: d.potapov@spbu.ru
Russia

Bibliografia

  1. Rakotoson, J.M. Generalized eigenvalue problems for totally discontinuous operators / J.M. Rakotoson // Disc. Contin. Dyn. Syst. — 2010. — V. 28, № 1. — P. 343-373.
  2. Chrayteh, H. Eigenvalue problems with fully discontinuous operators and critical exponents / H. Chrayteh, J.M. Rakotoson // Nonlin. Anal. — 2010. — V. 73, № 7. — P. 2036-2055.
  3. Chrayteh, H. Qualitative properties of eigenvectors related to multivalued operators and some existence results / H. Chrayteh // J. Optim. Theory Appl. — 2012. — V. 155, № 2. — P. 507-533.
  4. Pavlenko, V.N. and Potapov, D.K., Existence of a ray of eigenvalues for equations with discontinuous operators, Siberian Math. J., 2001, vol. 42, no. 4, pp. 766–773.
  5. Potapov, D.K., On an existence of a ray of eigenvalues for equations of elliptic type with discontinuous nonlinearities in a critical case, Vestn. Saint-Petersburg Univ. Ser. 10. Prikl. Mat. Inf. Protsessy Upr., 2004, no. 4, pp. 125–132.
  6. Potapov, D.K., On a number of solutions in problems with spectral parameter for equations with discontinuous operators, Ufa Math. J., 2013, vol. 5, no. 2, pp. 56–62.
  7. Potapov, D.K., Estimation of the bifurcation parameter in spectral problems for equations with discontinuous operators, Ufa Math. J., 2011, vol. 3, no. 1, pp. 42–44.
  8. Potapov, D.K., Estimation of operator norms in eigenvalue problems for equations with discontinuous operators, Izv. Saratovskogo Univ. Novaya ser. Ser. Mat. Mekh. Inf., 2011, vol. 11, no. 4, pp. 41–45.
  9. Potapov, D.K., On elliptic equations with spectral parameter and discontinuous nonlinearity, J. Sib. Fed. Univ. Math. & Phys., 2012, vol. 5, no. 3, pp. 417–421.
  10. Bonanno, G. Some remarks on a three critical points theorem / G. Bonanno // Nonlin. Anal. — 2003. — V. 54, № 4. — P. 651-665.
  11. Bonanno, G. Non-differentiable functionals and applications to elliptic problems with discontinuous nonlinearities / G. Bonanno, P. Candito // J. Differ. Equat. — 2008. — V. 244, № 12. — P. 3031-3059.
  12. Potapov, D.K., On an upper bound for the value of the bifurcation parameter in eigenvalue problems for elliptic equations with discontinuous nonlinearities, Differ. Equat., 2008, vol. 44, no. 5, pp. 737–739.
  13. Potapov, D.K., On the eigenvalue set structure for higher-order equations of elliptic type with discontinuous nonlinearities, Differ. Equat., 2010, vol. 46, no. 1, pp. 155–157.
  14. Potapov, D.K., Estimations of a differential operator in spectral parameter problems for elliptic equations with discontinuous nonlinearities, Vestn. Samarskogo Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 2010, no. 5 (21), pp. 268–271.
  15. Potapov, D.K., Existence of solutions, estimates for the differential operator, and a “separating” set in a boundary value problem for a second-order differential equation with a discontinuous nonlinearity, Differ. Equat., 2015, vol. 51, no. 7, pp. 967–972.

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