Existence and multiplicity of positive solutions for Neumann problems involving singularity and critical growth

2018 ◽  
Vol 459 (2) ◽  
pp. 959-979
Author(s):  
Chun-Yu Lei
Keyword(s):  
Positive Solutions ◽  
Critical Growth ◽  
Neumann Problems ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions

scholarly journals Positive Solutions for Schrödinger-Poisson Systems with Sign-Changing Potential and Critical Growth

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Pengfei He ◽  
Hongmin Suo
Keyword(s):  
Variational Method ◽  
Positive Solutions ◽  
Critical Growth ◽  
Existence And Multiplicity ◽  
Existence Of Positive Solutions ◽  
Multiplicity Of Positive Solutions

In this paper, we study the existence of positive solutions for Schrödinger-Poisson systems with sign-changing potential and critical growth. By using the analytic techniques and variational method, the existence and multiplicity of positive solutions are obtained.

scholarly journals On Dirichlet problem for fractional p-Laplacian with singular non-linearity

2016 ◽  
Vol 8 (1) ◽  
pp. 52-72 ◽  
Author(s):  
Tuhina Mukherjee ◽  
Konijeti Sreenadh
Keyword(s):  
Dirichlet Problem ◽  
Variational Methods ◽  
Bounded Domain ◽  
Positive Solutions ◽  
Smooth Boundary ◽  
Critical Growth ◽  
Laplacian Equation ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions

Abstract In this article, we study the following fractional p-Laplacian equation with critical growth and singular non-linearity: (-\Delta_{p})^{s}u=\lambda u^{-q}+u^{\alpha},\quad u>0\quad\text{in }\Omega,% \qquad u=0\quad\text{in }\mathbb{R}^{n}\setminus\Omega, where Ω is a bounded domain in {\mathbb{R}^{n}} with smooth boundary {\partial\Omega} , {n>sp} , {s\in(0,1)} , {\lambda>0} , {0<q\leq 1} and {1<p<\alpha+1\leq p^{*}_{s}} . We use variational methods to show the existence and multiplicity of positive solutions of the above problem with respect to the parameter λ.

Multiplicity of Positive Solutions for Critical Singular Elliptic Systems With Concave-Convex Nonlinearities

2009 ◽  
Vol 9 (2) ◽  
Author(s):  
Tsing-San Hsu
Keyword(s):  
Variational Methods ◽  
Elliptic System ◽  
Positive Solutions ◽  
Elliptic Systems ◽  
Critical Growth ◽  
Bounded Domains ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions

AbstractIn this paper, we consider a singular elliptic system with both concave-convex nonlinearities and critical growth terms in bounded domains. The existence and multiplicity results of positive solutions are obtained by variational methods.

Positive solutions of fractional elliptic equation with critical and singular nonlinearity

2017 ◽  
Vol 6 (3) ◽  
pp. 327-354 ◽  
Author(s):  
Jacques Giacomoni ◽  
Tuhina Mukherjee ◽  
Konijeti Sreenadh
Keyword(s):  
Elliptic Equation ◽  
Variational Methods ◽  
Bounded Domain ◽  
Positive Solutions ◽  
Smooth Boundary ◽  
Critical Growth ◽  
Content Type ◽  
Singular Nonlinearity ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions

AbstractIn this article, we study the following fractional elliptic equation with critical growth and singular nonlinearity:(-\Delta)^{s}u=u^{-q}+\lambda u^{{2^{*}_{s}}-1},\qquad u>0\quad\text{in }% \Omega,\qquad u=0\quad\text{in }\mathbb{R}^{n}\setminus\Omega,where Ω is a bounded domain in {\mathbb{R}^{n}} with smooth boundary {\partial\Omega}, {n>2s}, {s\in(0,1)}, {\lambda>0}, {q>0} and {2^{*}_{s}=\frac{2n}{n-2s}}. We use variational methods to show the existence and multiplicity of positive solutions with respect to the parameter λ.

Multiplicity of positive solutions for a class of problems with critical growth in ℝN

2009 ◽  
Vol 52 (1) ◽  
pp. 1-21 ◽  
Author(s):  
Claudianor O. Alves ◽  
Daniel C. de Morais Filho ◽  
Marco A. S. Souto
Keyword(s):  
Variational Methods ◽  
Positive Solutions ◽  
Continuous Functions ◽  
Critical Growth ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions ◽  
Image Position

AbstractUsing variational methods, we establish the existence and multiplicity of positive solutions for the following class of problems:where λ,β∈(0,∞), q∈(1,2*−1), 2*=2N/(N−2), N≥3, V,Z:ℝN→ℝ are continuous functions verifying some hypotheses.

scholarly journals Positive Solutions for a Class of Nonlinear Singular Fractional Differential Systems with Riemann–Stieltjes Coupled Integral Boundary Value Conditions

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 107
Author(s):  
Daliang Zhao ◽  
Juan Mao
Keyword(s):  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Main Tool ◽  
Integral Boundary ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Existence And Multiplicity ◽  
Fractional Differential ◽  
Multiplicity Of Positive Solutions

In this paper, sufficient conditions ensuring existence and multiplicity of positive solutions for a class of nonlinear singular fractional differential systems are derived with Riemann–Stieltjes coupled integral boundary value conditions in Banach Spaces. Nonlinear functions f(t,u,v) and g(t,u,v) in the considered systems are allowed to be singular at every variable. The boundary conditions here are coupled forms with Riemann–Stieltjes integrals. In order to overcome the difficulties arising from the singularity, a suitable cone is constructed through the properties of Green’s functions associated with the systems. The main tool used in the present paper is the fixed point theorem on cone. Lastly, an example is offered to show the effectiveness of our obtained new results.

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