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Nonpositive solutions of one functional differential inequality

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Nonlinear Oscillations

We establish efficient conditions guaranteeing that every solution of the problem

$ u'(t) \geq \ell (u)(t),\quad u(a) \geq h(u), $

where \( \ell :C\left( {\left[ {a,b} \right];\mathbb{R}} \right) \to L\left( {\left[ {a,b} \right];\mathbb{R}} \right) \) and \( h:C\left( {\left[ {a,b} \right];\mathbb{R}} \right) \to \mathbb{R} \) are linear bounded operators, is nonpositive. The results obtained are very useful for the investigation of the question of solvability and unique solvability of nonlocal boundary-value problems for first-order functional differential equations in both linear and nonlinear cases.

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Authors and Affiliations

  1. Masaryk University, Brno, Czech Republic

    A. Lomtatidze

  2. Institute of Mathematics, Brno, Czech Republic

    Z. Opluštil

  3. Institute of Mathematics, Academy of Sciences of the Czech Republic, Brno, Czech Republic

    J. Šremr

Authors
  1. A. Lomtatidze
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  2. Z. Opluštil
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  3. J. Šremr
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Corresponding author

Correspondence to A. Lomtatidze.

Additional information

Published in Neliniini Kolyvannya, Vol. 12, No. 4, pp. 461–494, October–December, 2009.

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Lomtatidze, A., Opluštil, Z. & Šremr, J. Nonpositive solutions of one functional differential inequality. Nonlinear Oscill 12, 474–509 (2009). https://doi.org/10.1007/s11072-010-0090-4

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  • DOI: https://doi.org/10.1007/s11072-010-0090-4

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