The effect of the domain topology on the number of positive solutions of nonlinear elliptic problems

1991 ◽  
Vol 114 (1) ◽  
pp. 79-93 ◽  
Author(s):  
Vieri Benci ◽  
Giovanna Cerami
Keyword(s):  
Positive Solutions ◽  
Elliptic Problems ◽  
Nonlinear Elliptic Problems ◽  
Nonlinear Elliptic

Positive solutions of strongly nonlinear elliptic problems

2015 ◽  
Vol 93 (1-2) ◽  
pp. 1-20 ◽  
Author(s):  
Francisco Julio S.A. Corrêa ◽  
Marcos L. Carvalho ◽  
J.V.A. Goncalves ◽  
Kaye O. Silva
Keyword(s):  
Positive Solutions ◽  
Elliptic Problems ◽  
Nonlinear Elliptic Problems ◽  
Strongly Nonlinear ◽  
Nonlinear Elliptic

Multiplicity of positive and nodal solutions for nonlinear elliptic problems in RN

1998 ◽  
Vol 128 (5) ◽  
pp. 1069-1097 ◽  
Author(s):  
Ziqing Xie
Keyword(s):  
Positive Solutions ◽  
Elliptic Problems ◽  
Nodal Solutions ◽  
Nonlinear Elliptic Problems ◽  
Nonlinear Elliptic ◽  
Image Position

We consider the following problem:wherefor x ∈ RN, f(x, t), ft (x, t) ∈ C(RN × R), and f (x, t) ≧ 0 for all x ∈ RN and t ∈ R+, f(x, t) is an odd function of t. We show that if the maximum of Q(x) is achieved at k different points of RN, then for μ large enough the above problem has at least k positive solutions and k nodal solutions.

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