Pseudomonotonicity and nonlinear hyperbolic equations

Dimitrios A. Kandilakis

Commentationes Mathematicae Universitatis Carolinae (1997)

  • Volume: 38, Issue: 3, page 463-469
  • ISSN: 0010-2628

Abstract

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In this paper we consider a nonlinear hyperbolic boundary value problem. We show that this problem admits weak solutions by using a lifting result for pseudomonotone operators and a surjectivity result concerning coercive and monotone operators.

How to cite

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Kandilakis, Dimitrios A.. "Pseudomonotonicity and nonlinear hyperbolic equations." Commentationes Mathematicae Universitatis Carolinae 38.3 (1997): 463-469. <http://eudml.org/doc/248105>.

@article{Kandilakis1997,
abstract = {In this paper we consider a nonlinear hyperbolic boundary value problem. We show that this problem admits weak solutions by using a lifting result for pseudomonotone operators and a surjectivity result concerning coercive and monotone operators.},
author = {Kandilakis, Dimitrios A.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {pseudomonotone operator; demicontinuous operator; maximal monotone operator; weak solution; pseudomonotone operator; demicontinuous operator; maximal monotone operator},
language = {eng},
number = {3},
pages = {463-469},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Pseudomonotonicity and nonlinear hyperbolic equations},
url = {http://eudml.org/doc/248105},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Kandilakis, Dimitrios A.
TI - Pseudomonotonicity and nonlinear hyperbolic equations
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 3
SP - 463
EP - 469
AB - In this paper we consider a nonlinear hyperbolic boundary value problem. We show that this problem admits weak solutions by using a lifting result for pseudomonotone operators and a surjectivity result concerning coercive and monotone operators.
LA - eng
KW - pseudomonotone operator; demicontinuous operator; maximal monotone operator; weak solution; pseudomonotone operator; demicontinuous operator; maximal monotone operator
UR - http://eudml.org/doc/248105
ER -

References

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  1. Ash R., Analysis and Probability, Academic Press, NY, 1972. 
  2. Barbu V., Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff Inter. Pub. Leyden, The Netherlands. Zbl0328.47035MR0390843
  3. Gossez J.-P., Mustonen V., Pseudomonotonicity and the Leray-Lions condition, Diff. and Integral Equations 6 (1993), 37-45. (1993) MR1190164
  4. Lions J.-L., Quelques Methodes de Resolution des Problemes aux Limites Non-Lineaires, Dunod, Paris, 1969. Zbl0248.35001MR0259693
  5. Papageorgiou N.S., Existence of solutions for second order evolution inclusions, J. Appl. Math and Stoch. Anal. 4, vol. 7 (1994), pp.525-535. Zbl0857.34028MR1310925
  6. Ton B.-A., Nonlinear evolution equations in Banach spaces, J. Diff. Equations 9 (1971), 608-618. (1971) Zbl0227.47043MR0300172
  7. Zeidler E., Nonlinear Functional Analysis and its Applications, Springer Verlag, NY, 1990. Zbl0794.47033

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