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 Existence of Positive Solutions for a System of Singular Fractional Boundary Value Problems with p-Laplacian Operators

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1890
Author(s):  
Ahmed Alsaedi ◽  
Rodica Luca ◽  
Bashir Ahmad
Keyword(s):  
Positive Solutions ◽  
Fractional Derivatives ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Existence And Multiplicity ◽  
Existence Of Positive Solutions ◽  
Fractional Differential ◽  
Multiplicity Of Positive Solutions ◽  
Laplacian Operators ◽  
Fractional Boundary Value Problems

We investigate the existence and multiplicity of positive solutions for a system of Riemann–Liouville fractional differential equations with singular nonnegative nonlinearities and p-Laplacian operators, subject to nonlocal boundary conditions which contain fractional derivatives and Riemann–Stieltjes integrals.

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.

scholarly journals Multiple positive solutions for a logarithmic Schrödinger–Poisson system with singular nonelinearity

2021 ◽  
pp. 1-15
Author(s):  
Linyan Peng ◽  
Hongmin Suo ◽  
Deke Wu ◽  
Hongxi Feng ◽  
Chunyu Lei
Keyword(s):  
Variational Method ◽  
Critical Point ◽  
Positive Solutions ◽  
Critical Point Theory ◽  
Point Theory ◽  
Multiple Positive Solutions ◽  
Poisson System ◽  
Smooth Bounded Domain ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions

In this article, we devote ourselves to investigate the following logarithmic Schrödinger–Poisson systems with singular nonlinearity { − Δ u + ϕ u = | u | p−2 u log ⁡ | u | + λ u γ , i n   Ω , − Δ ϕ = u 2 , i n   Ω , u = ϕ = 0 , o n   ∂ Ω , where Ω is a smooth bounded domain with boundary 0 < γ < 1 , p ∈ ( 4 , 6 ) and λ > 0 is a real parameter. By using the critical point theory for nonsmooth functional and variational method, the existence and multiplicity of positive solutions are established.

scholarly journals Multiplicity of Weak Positive Solutions for Fractional p & q Laplacian Problem with Singular Nonlinearity

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Dandan Yang ◽  
Chuanzhi Bai
Keyword(s):  
Variational Method ◽  
Positive Solutions ◽  
Nehari Manifold ◽  
Analysis Techniques ◽  
Singular Nonlinearity ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions

In this paper, we prove the existence and multiplicity of positive solutions for a class of fractional p & q Laplacian problem with singular nonlinearity. Our approach relies on the variational method, some analysis techniques, and the method of Nehari manifold.

scholarly journals On the Elliptic Problems Involving Multisingular Inverse Square Potentials and Concave-Convex Nonlinearities

2011 ◽  
Vol 2011 ◽  
pp. 1-22
Author(s):  
Tsing-San Hsu
Keyword(s):  
Variational Method ◽  
Positive Solutions ◽  
Elliptic Problem ◽  
Elliptic Problems ◽  
Existence And Multiplicity ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Hardy Type ◽  
Multiplicity Of Positive Solutions ◽  
Inverse Square Potentials

A semilinear elliptic problem with concave-convex nonlinearities and multiple Hardy-type terms is considered. By means of a variational method, we establish the existence and multiplicity of positive solutions for problem .

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.

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