The branch of positive solutions to a semilinear elliptic equation on $\mathbb {R}^N$

H. Jeanjean; M. Lucia; C. A. Stuart

The branch of positive solutions to a semilinear elliptic equation on $ℝ^{N}$

H. Jeanjean; M. Lucia; C. A. Stuart

Rendiconti del Seminario Matematico della Università di Padova (1999)

Volume: 101, page 229-262
ISSN: 0041-8994

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Jeanjean, H., Lucia, M., and Stuart, C. A.. "The branch of positive solutions to a semilinear elliptic equation on $\mathbb {R}^N$." Rendiconti del Seminario Matematico della Università di Padova 101 (1999): 229-262. <http://eudml.org/doc/108488>.

@article{Jeanjean1999,
author = {Jeanjean, H., Lucia, M., Stuart, C. A.},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {supersolutions; explicit bounds; global behaviour},
language = {eng},
pages = {229-262},
publisher = {Seminario Matematico of the University of Padua},
title = {The branch of positive solutions to a semilinear elliptic equation on $\mathbb \{R\}^N$},
url = {http://eudml.org/doc/108488},
volume = {101},
year = {1999},
}

TY - JOUR
AU - Jeanjean, H.
AU - Lucia, M.
AU - Stuart, C. A.
TI - The branch of positive solutions to a semilinear elliptic equation on $\mathbb {R}^N$
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1999
PB - Seminario Matematico of the University of Padua
VL - 101
SP - 229
EP - 262
LA - eng
KW - supersolutions; explicit bounds; global behaviour
UR - http://eudml.org/doc/108488
ER -

References

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[1] A. Ambrosetti - J.L. Gámez, Branches of positive solutions for some semilinear Schrödinger equations, Math. Z., 224 (1997), pp. 347-362. Zbl0956.35039 MR1439195
[2] H. Brézis, Analyse fonctionnelle, Masson, Paris (1983). Zbl0511.46001 MR697382
[3] A.L. Edelson - C.A. Stuart, The principal branch of solutions of a nonlinear elliptic eigenvalue problem on RN, J. Differential Equations, 124 (1996), pp. 279-301. Zbl0842.35029 MR1370142
[4] P.M. Fitzpatrick - J. Pejsachowicz - P.J. Rabier, The degree of proper C2 Fredholm mappings, J. reine angew. Math., 427 (1992), pp. 1-33. Zbl0745.47049 MR1162430
[5] D. Gildarg - N.S. Trudinger, Elliptic partial differential equations of second order, volume 224 of Die Grundehren der mathematischen Wissenschaften in Einzeldarstellungen, Springer Verlag, Berlin (1983). Zbl0562.35001 MR737190
[6] H. Jeanjean - M. Lucia - C.A. Stuart, Branches of solutions to semilinear elliptic equations on RN, Math. Z., 230 (1999), pp. 79-105. Zbl0955.35058 MR1671862
[7] B. Kawohl, Rearrangements and convexity of levels sets in PDE, Lecture Notes in Mathematics, 1150, Springer-Verlag, Berlin (1985). Zbl0593.35002 MR810619
[8] P.H. Rabinowitz, Some global results for nonlinear eigenvalues problems, J. Func. Anal., 7 (1971), pp. 487-513. Zbl0212.16504 MR301587
[9] C.A. Stuart, Global properties of components of solutions of nonlinear second order ordinary differential equations on the half-line, Ann. Sc. Norm. Sup. PisaII (1975), pp. 265-286. Zbl0326.34034 MR380013

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