scholarly journals Pairs of Nodal Solutions for a Class of Nonlinear Problems with One-sided Growth Conditions

2013 ◽  
Vol 13 (1) ◽  
Author(s):  
Alberto Boscaggin ◽  
Fabio Zanolin
Keyword(s):  
Weight Function ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Nonlinear Problems ◽  
Growth Conditions ◽  
Second Order ◽  
Nodal Solutions ◽  
Multiplicity Results ◽  
Sturm Liouville ◽  
Growth Restrictions

AbstractBoundary value problems of Sturm-Liouville and periodic type for the second order nonlinear ODE uʺ + λf(t, u) = 0 are considered. Multiplicity results are obtained, for λ positive and large, under suitable growth restrictions on f(t, u) of superlinear type at u = 0 and of sublinear type at u = ∞. Only one-sided growth conditions are required. Applications are given to the equation uʺ + λq(t)f(u) = 0, allowing also a weight function q(t) of nonconstant sign.

Bounds for distance between eigenvalues of boundary value problems with retarded argument

2019 ◽  
Vol 69 (2) ◽  
pp. 399-408
Author(s):  
Erdoğan Şen
Keyword(s):  
Boundary Condition ◽  
Weight Function ◽  
Boundary Value Problems ◽  
Liouville Operator ◽  
Boundary Value ◽  
Physical Parameters ◽  
Retarded Argument ◽  
Transmission Coefficients ◽  
Sturm Liouville ◽  
Special Case

Abstract In this study we are concerned with spectrum of boundary value problems with retarded argument with discontinuous weight function, two supplementary transmission conditions at the point of discontinuity, spectral and physical parameters in the boundary condition and we obtain bounds for the distance between eigenvalues. We extend and generalize some approaches and results of the classical regular and discontinuous Sturm-Liouville problems. In the special case that ω (x) ≡ 1, the transmission coefficients γ1 = δ1, γ2 = δ2 and retarded argument Δ ≡ 0 in the results obtained in this work coincide with corresponding results in the classical Sturm-Liouville operator.

scholarly journals Nodal Solutions for Some Second-Order Semipositone Integral Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Huiqin Lu ◽  
Yang Wang ◽  
Yansheng Liu
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Global Bifurcation ◽  
Second Order ◽  
Nodal Solutions ◽  
Integral Boundary ◽  
Bifurcation Theorem ◽  
Existence And Multiplicity ◽  
Integral Boundary Value Problems

Using bifurcation techniques, we first prove a global bifurcation theorem for nonlinear second-order semipositone integral boundary value problems. Then the existence and multiplicity of nodal solutions of the above problems are obtained. Finally, an example is worked out to illustrate our main results.

scholarly journals Multiplicity of positive solutions for second order Sturm-Liouville boundary value problems

2016 ◽  
Vol 25 (2) ◽  
pp. 215-222
Author(s):  
K. R. PRASAD ◽  
◽  
N. SREEDHAR ◽  
L. T. WESEN ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Multiple Positive Solutions ◽  
Sturm Liouville ◽  
Multiplicity Of Positive Solutions

In this paper, we develop criteria for the existence of multiple positive solutions for second order Sturm-Liouville boundary value problem, u 00 + k 2u + f(t, u) = 0, 0 ≤ t ≤ 1, au(0) − bu0 (0) = 0 and cu(1) + du0 (1) = 0, where k ∈ 0, π 2 is a constant, by an application of Avery–Henderson fixed point theorem.

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].

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