scholarly journals POSITIVE SOLUTIONS TO p-KIRCHHOFF-TYPE ELLIPTIC EQUATION WITH GENERAL SUBCRITICAL GROWTH

2017 ◽  
Vol 54 (3) ◽  
pp. 1023-1036
Author(s):  
Huixing Zhang ◽  
Ran Zhang
Keyword(s):  
Elliptic Equation ◽  
Positive Solutions ◽  
Subcritical Growth ◽  
Kirchhoff Type

Positive solutions of Kirchhoff-type non-local elliptic equation: a bifurcation approach

2017 ◽  
Vol 147 (4) ◽  
pp. 875-894 ◽  
Author(s):  
Zhanping Liang ◽  
Fuyi Li ◽  
Junping Shi
Keyword(s):  
Elliptic Equation ◽  
Eigenvalue Problem ◽  
Positive Solutions ◽  
Nonlinear Eigenvalue Problem ◽  
Global Bifurcation ◽  
Integral Term ◽  
Kirchhoff Type ◽  
Nonlinear Elliptic ◽  
Linear Eigenvalue Problem ◽  
Non Local

Positive solutions of a Kirchhoff-type nonlinear elliptic equation with a non-local integral term on a bounded domain in ℝN, N ⩾ 1, are studied by using bifurcation theory. The parameter regions of existence, non-existence and uniqueness of positive solutions are characterized by the eigenvalues of a linear eigenvalue problem and a nonlinear eigenvalue problem. Local and global bifurcation diagrams of positive solutions for various parameter regions are obtained.

scholarly journals On an elliptic equation of p-Kirchhoff type via variational methods

2006 ◽  
Vol 74 (2) ◽  
pp. 263-277 ◽  
Author(s):  
Francisco Júlio ◽  
S. A. Corrêa ◽  
Giovany M. Figueiredo
Keyword(s):  
Elliptic Equation ◽  
Variational Methods ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Nonlocal Boundary ◽  
Continuous Functions ◽  
Bounded Smooth Domain ◽  
Kirchhoff Type ◽  
Existence Of Positive Solutions ◽  
Bounded Smooth

This paper is concerned with the existence of positive solutions to the class of nonlocal boundary value problems of the p-Kirchhoff type and where Ω is a bounded smooth domain of ℝN, 1 < p < N, s ≥ p* = (pN)/(N – p) and M and f are continuous functions.

scholarly journals A multiplicity result for a (p, q)-Schrödinger–Kirchhoff type equation

2021 ◽  
Author(s):  
Vincenzo Ambrosio ◽  
Teresa Isernia
Keyword(s):  
Variational Methods ◽  
Positive Solutions ◽  
Category Theory ◽  
Type Equation ◽  
Multiplicity Result ◽  
Positive Potential ◽  
Subcritical Growth ◽  
Kirchhoff Type ◽  
Kirchhoff Type Equation ◽  
Penalization Techniques

AbstractIn this paper, we study a class of (p, q)-Schrödinger–Kirchhoff type equations involving a continuous positive potential satisfying del Pino–Felmer type conditions and a continuous nonlinearity with subcritical growth at infinity. By applying variational methods, penalization techniques and Lusternik–Schnirelman category theory, we relate the number of positive solutions with the topology of the set where the potential attains its minimum values.

scholarly journals On the Existence of Solutions of a Nonlocal Elliptic Equation with ap-Kirchhoff-Type Term

2008 ◽  
Vol 2008 ◽  
pp. 1-25 ◽  
Author(s):  
Francisco Julio S. A. Corrêa ◽  
Rúbia G. Nascimento
Keyword(s):  
Elliptic Equation ◽  
Positive Solutions ◽  
Existence Of Solutions ◽  
Elliptic Problems ◽  
Smooth Domain ◽  
Bounded Smooth Domain ◽  
Kirchhoff Type ◽  
Existence Of Positive Solutions ◽  
Bounded Smooth

Questions on the existence of positive solutions for the following class of elliptic problems are studied:−[M(‖u‖1,pp)]1,pΔpu=f(x,u), inΩ,u=0, on∂Ω, whereΩ⊂ℝNis a bounded smooth domain,f:Ω¯×ℝ+→ℝandM:ℝ+→ℝ,  ℝ+=[0,∞)are given functions.

scholarly journals The existence of positive solutions for Kirchhoff-type problems via the sub-supersolution method

2018 ◽  
Vol 26 (1) ◽  
pp. 5-41 ◽  
Author(s):  
Baoqiang Yan ◽  
Donal O’Regan ◽  
Ravi P. Agarwal
Keyword(s):  
Positive Solutions ◽  
Bifurcation Theory ◽  
Sufficient Conditions ◽  
Global Bifurcation ◽  
Existence Of A Solution ◽  
Kirchhoff Type ◽  
Existence Of Positive Solutions ◽  
Global Bifurcation Theory ◽  
Necessary And Sufficient ◽  
Kirchhoff Type Problems

Abstract In this paper we discuss the existence of a solution between wellordered subsolution and supersolution of the Kirchhoff equation. Using the sub-supersolution method together with a Rabinowitz-type global bifurcation theory, we establish the existence of positive solutions for Kirchhoff-type problems when the nonlinearity is singular or sign-changing. Moreover, we obtain some necessary and sufficient conditions for the existence of positive solutions for the problem when N = 1.

Positive Solutions for the Generalized Nonlinear Logistic Equations

2016 ◽  
Vol 59 (01) ◽  
pp. 73-86 ◽  
Author(s):  
Leszek Gasiński ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Differential Operator ◽  
Elliptic Equation ◽  
Positive Solutions ◽  
Type Result ◽  
Logistic Equations ◽  
Nonhomogeneous Differential Operator

AbstractWe consider a nonlinear parametric elliptic equation driven by a nonhomogeneous differential operator with a logistic reaction of the superdiòusive type. Using variationalmethods coupled with suitable truncation and comparison techniques, we prove a bifurcation type result describing the set of positive solutions as the parameter varies.

Positive solutions to a semilinear elliptic equation with a Sobolev–Hardy term

2011 ◽  
Vol 74 (14) ◽  
pp. 4847-4861 ◽  
Author(s):  
Ali Al-aati ◽  
Chunhua Wang ◽  
Jing Zhao
Keyword(s):  
Elliptic Equation ◽  
Positive Solutions ◽  
Semilinear Elliptic Equation ◽  
Semilinear Elliptic ◽  
Hardy Term
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