An existence result for nonlinear evolution equations of second order

Dimitrios A. Kandilakis

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (1996)

  • Volume: 16, Issue: 2, page 153-160
  • ISSN: 1509-9407

Abstract

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In this paper we consider a second order differential equation involving the difference of two monotone operators. Using an auxiliary equation, a priori bounds and a compactness argument we show that the differential equation has a local solution. An example is also presented in detail.

How to cite

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Dimitrios A. Kandilakis. "An existence result for nonlinear evolution equations of second order." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 16.2 (1996): 153-160. <http://eudml.org/doc/275877>.

@article{DimitriosA1996,
abstract = {In this paper we consider a second order differential equation involving the difference of two monotone operators. Using an auxiliary equation, a priori bounds and a compactness argument we show that the differential equation has a local solution. An example is also presented in detail.},
author = {Dimitrios A. Kandilakis},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {a priori bound; maximal monotone operator; coercive operator; compact embedding; difference of two monotone operators},
language = {eng},
number = {2},
pages = {153-160},
title = {An existence result for nonlinear evolution equations of second order},
url = {http://eudml.org/doc/275877},
volume = {16},
year = {1996},
}

TY - JOUR
AU - Dimitrios A. Kandilakis
TI - An existence result for nonlinear evolution equations of second order
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 1996
VL - 16
IS - 2
SP - 153
EP - 160
AB - In this paper we consider a second order differential equation involving the difference of two monotone operators. Using an auxiliary equation, a priori bounds and a compactness argument we show that the differential equation has a local solution. An example is also presented in detail.
LA - eng
KW - a priori bound; maximal monotone operator; coercive operator; compact embedding; difference of two monotone operators
UR - http://eudml.org/doc/275877
ER -

References

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  2. [2] C. Bardos, H. Brezis, Sur une classe de problemes d'évolution non linéaires, J. Diff. Equations 6 (1969), 345-394. Zbl0176.09003
  3. [3] E. Di Benedetto R.E. Showalter, Implicit degenerate evolution equations and applications, SIAM J. Math. Anal. 12 (1981), 731-751. Zbl0477.47037
  4. [4] F. Bernis, Existence results for doubly nonlinear higher order parabolic equations on unbounded domains, Math. Ann. 279 (1988), 373-394. Zbl0609.35048
  5. [5] P. Colli, A. Visintin, On a class of doubly nonlinear evolution equations, Commun. in Partial Diff. Eq. 15 (1990), 737-756. Zbl0707.34053
  6. [6] G. Duvaut J.L. Lions, Sur de nouveaux problemes d'inéquations variationnelles posés par la Mécanique, C.R. Acad. Sc. Paris, 269 (1969), 570-572. Zbl0193.07702
  7. [7] O. Grange F. Mignot, Sur la résolution d'une équation et d'une inéquation paraboliques non linéaires, J. Funct. Anal. 11 (1972), 77-92. Zbl0251.35055
  8. [8] H. Monch, Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces, Nonlinear Analysis TMA 4 (1980), 985-999. Zbl0462.34041
  9. [9] P.A. Raviart, Sur la résolution de certaines equations paraboliques non linéaires, J. Funct. Anal. 5 (1970), 299-328. Zbl0199.42401

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