scholarly journals Exact Multiplicity Results for a Class of Boundary-Value Problems with Cubic Nonlinearities

1995 ◽  
Vol 194 (1) ◽  
pp. 328-341 ◽  
Author(s):  
P. Korman ◽  
T.C. Ouyang
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Multiplicity Results ◽  
Exact Multiplicity

scholarly journals Exact Multiplicity of Sign-Changing Solutions for a Class of Second-Order Dirichlet Boundary Value Problem with Weight Function

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Yulian An
Keyword(s):  
Boundary Value Problem ◽  
Weight Function ◽  
Boundary Value Problems ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Constant Sign ◽  
Dirichlet Boundary Value Problem ◽  
Multiplicity Results ◽  
Sign Changing Solutions ◽  
Exact Multiplicity

Using bifurcation techniques and Sturm comparison theorem, we establish exact multiplicity results of sign-changing or constant sign solutions for the boundary value problemsu″+a(t)f(u)=0,t∈(0,1),u(0)=0, andu(1)=0, wheref∈C(ℝ,ℝ)satisfiesf(0)=0and the limitsf∞=lim|s|→∞(f(s)/s),f0=lim|s|→0(f(s)/s)∈{0,∞}. Weight functiona(t)∈C1[0,1]satisfiesa(t)>0on[0,1].

Exact multiplicity results for boundary value problems with nonlinearities generalising cubic

1996 ◽  
Vol 126 (3) ◽  
pp. 599-616 ◽  
Author(s):  
Philip Korman ◽  
Yi Li ◽  
Tiancheng Ouyang
Keyword(s):  
Boundary Value Problems ◽  
Bifurcation Theory ◽  
Boundary Value ◽  
Multiplicity Results ◽  
Image Position ◽  
Exact Multiplicity

Using techniques of bifurcation theory we present two exact multiplicity results for boundary value problems of the typeThe first result concerns the case when the nonlinearity is independent of x and behaves like a cubic in u. The second one deals with a class of nonlinearities with explicit x dependence.

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