scholarly journals Multiplicity results for a fractional Kirchhoff equation involving sign-changing weight function

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Chuanzhi Bai
Keyword(s):  
Weight Function ◽  
Kirchhoff Equation ◽  
Multiplicity Results ◽  
Fractional Kirchhoff Equation

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.

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].

scholarly journals EXISTENCE OF MULTIPLE POSITIVE SOLUTIONS FOR QUASILINEAR ELLIPTIC SYSTEMS INVOLVING CRITICAL HARDY–SOBOLEV EXPONENTS AND SIGN-CHANGING WEIGHT FUNCTION

2012 ◽  
Vol 17 (3) ◽  
pp. 330-350 ◽  
Author(s):  
Nemat Nyamoradi
Keyword(s):  
Weight Function ◽  
Variational Methods ◽  
Positive Solutions ◽  
Elliptic Systems ◽  
Multiple Positive Solutions ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Quasilinear Elliptic Systems ◽  
Sobolev Exponent ◽  
Quasilinear Elliptic

In this paper, we consider a class of quasilinear elliptic systems with weights and the nonlinearity involving the critical Hardy–Sobolev exponent and one sign-changing function. The existence and multiplicity results of positive solutions are obtained by variational methods.

scholarly journals On the compactness threshold in the critical Kirchhoff equation

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Erisa Hasani ◽  
Kanishka Perera
Keyword(s):  
Closed Form ◽  
Threshold Level ◽  
Kirchhoff Equation ◽  
Nonlocal Term ◽  
Main Difficulty ◽  
Variational Characterization ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Closed Form Formula

<p style='text-indent:20px;'>We study a class of critical Kirchhoff problems with a general nonlocal term. The main difficulty here is the absence of a closed-form formula for the compactness threshold. First we obtain a variational characterization of this threshold level. Then we prove a series of existence and multiplicity results based on this variational characterization.</p>

scholarly journals Existence and multiplicity results for fractional p-Kirchhoff equation with sign changing nonlinearities

2016 ◽  
Vol 7 (2) ◽  
Author(s):  
Pawan K. Mishra ◽  
Konijeti Sreenadh
Keyword(s):  
Kirchhoff Equation ◽  
Multiplicity Results ◽  
Existence And Multiplicity

AbstractIn this paper, we show the existence and multiplicity of nontrivial non-negative solutions of the fractional

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