Remarks on the Existence of Many Solutions of Certain Nonlinear Elliptic Equations

Edward N. Dancer; Shusen Yan

Bollettino dell'Unione Matematica Italiana (2007)

  • Volume: 10-B, Issue: 3, page 1013-1023
  • ISSN: 0392-4033

Abstract

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We show how a change of variable and peak solution methods can be used to prove that a number of nonlinear elliptic partial differential equations have many solutions.

How to cite

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Dancer, Edward N., and Yan, Shusen. "Remarks on the Existence of Many Solutions of Certain Nonlinear Elliptic Equations." Bollettino dell'Unione Matematica Italiana 10-B.3 (2007): 1013-1023. <http://eudml.org/doc/290427>.

@article{Dancer2007,
abstract = {We show how a change of variable and peak solution methods can be used to prove that a number of nonlinear elliptic partial differential equations have many solutions.},
author = {Dancer, Edward N., Yan, Shusen},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {1013-1023},
publisher = {Unione Matematica Italiana},
title = {Remarks on the Existence of Many Solutions of Certain Nonlinear Elliptic Equations},
url = {http://eudml.org/doc/290427},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Dancer, Edward N.
AU - Yan, Shusen
TI - Remarks on the Existence of Many Solutions of Certain Nonlinear Elliptic Equations
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/10//
PB - Unione Matematica Italiana
VL - 10-B
IS - 3
SP - 1013
EP - 1023
AB - We show how a change of variable and peak solution methods can be used to prove that a number of nonlinear elliptic partial differential equations have many solutions.
LA - eng
UR - http://eudml.org/doc/290427
ER -

References

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  4. DANCER, E. N., A note on asymptotic uniqueness for some nonlinearities which change sign, Bull Austral Math. Soc., 61 (2000), 305-312. Zbl0945.35031MR1748710DOI10.1017/S0004972700022309
  5. DANCER, E.N. - WEI, J., On the profile of solutions with two sharp layers to a singularly perturbed semilinear Dirichlet problem, Proc. Royal Soc. (Edinburgh)127A (1997), 691-701. Zbl0882.35052MR1465415DOI10.1017/S0308210500023775
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  9. DANCER, E. N. - YAN, SHUSEN, On the profile of the changing sign mountain pass solution for an elliptic problem, Trans. Amer. Math. Soc., 354 (2002), 3573-3600. Zbl1109.35041MR1911512DOI10.1090/S0002-9947-02-03026-X
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  14. SAUT, J. - TEMAN, R., Generic properties of nonlinear boundary value problems, Comm. Partial Diff. Eqns., 4 (1979), 293-319. Zbl0462.35016MR522714DOI10.1080/03605307908820096
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