The existence of positive solutions for an elliptic boundary value problem
2005 ◽
Vol 2005
(13)
◽
pp. 2005-2010
Keyword(s):
By using the mountain pass lemma, we study the existence of positive solutions for the equation−Δu(x)=λ(u|u|+u)(x)forx∈Ωtogether with Dirichlet boundary conditions and show that for everyλ<λ1, whereλ1is the first eigenvalue of−Δu=λuinΩwith the Dirichlet boundary conditions, the equation has a positive solution while no positive solution exists forλ≥λ1.
2006 ◽
Vol 11
(4)
◽
pp. 323-329
◽
2016 ◽
Vol 6
(4)
◽
pp. 17-22
2008 ◽
Vol 338
(2)
◽
pp. 885-891
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1998 ◽
Vol 58
(2)
◽
pp. 333-344
◽
1999 ◽
Vol 155
(2)
◽
pp. 423-442
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