Further results of existence of positive solutions of elliptic Kirchhoff equation with general nonlinearity of source terms

2020 ◽  
Vol 43 (15) ◽  
pp. 9195-9205
Author(s):  
Salah Boulaaras ◽  
Youcef Bouizem ◽  
Rafik Guefaifia
Keyword(s):  
Positive Solutions ◽  
Kirchhoff Equation ◽  
Source Terms ◽  
Existence Of Positive Solutions ◽  
General Nonlinearity

scholarly journals Schrödinger–Poisson systems with a general critical nonlinearity

2016 ◽  
Vol 19 (04) ◽  
pp. 1650028 ◽  
Author(s):  
Jianjun Zhang ◽  
João Marcos do Ó ◽  
Marco Squassina
Keyword(s):  
Positive Solutions ◽  
Critical Growth ◽  
Critical Nonlinearity ◽  
Poisson System ◽  
Asymptotics Of Solutions ◽  
Existence Of Positive Solutions ◽  
General Nonlinearity

We consider a Schrödinger–Poisson system involving a general nonlinearity at critical growth and we prove the existence of positive solutions. The Ambrosetti–Rabinowitz condition is not required. We also study the asymptotics of solutions with respect to a parameter.

scholarly journals Fractional Schrödinger–Poisson Systems with a General Subcritical or Critical Nonlinearity

2016 ◽  
Vol 16 (1) ◽  
pp. 15-30 ◽  
Author(s):  
Jianjun Zhang ◽  
João Marcos do Ó ◽  
Marco Squassina
Keyword(s):  
Positive Solutions ◽  
Critical Case ◽  
Perturbation Approach ◽  
Critical Nonlinearity ◽  
Poisson System ◽  
Asymptotics Of Solutions ◽  
Existence Of Positive Solutions ◽  
General Nonlinearity

AbstractWe consider a fractional Schrödinger–Poisson system with a general nonlinearity in the subcritical and critical case. The Ambrosetti–Rabinowitz condition is not required. By using a perturbation approach, we prove the existence of positive solutions. Moreover, we study the asymptotics of solutions for a vanishing parameter.

On Positive Solutions for Some Nonlinear Semipositone Elliptic Boundary Value

2006 ◽  
Vol 11 (4) ◽  
pp. 323-329 ◽  
Author(s):  
G. A. Afrouzi ◽  
S. H. Rasouli
Keyword(s):  
Boundary Value Problems ◽  
Positive Solution ◽  
Bounded Domain ◽  
Positive Solutions ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Laplacian Operator ◽  
Smooth Bounded Domain ◽  
Elliptic Boundary Value ◽  
Existence Of Positive Solutions

This study concerns the existence of positive solutions to classes of boundary value problems of the form−∆u = g(x,u), x ∈ Ω,u(x) = 0, x ∈ ∂Ω,where ∆ denote the Laplacian operator, Ω is a smooth bounded domain in RN (N ≥ 2) with ∂Ω of class C2, and connected, and g(x, 0) < 0 for some x ∈ Ω (semipositone problems). By using the method of sub-super solutions we prove the existence of positive solution to special types of g(x,u).

scholarly journals Existence of Positive Solutions for a Kind of Fractional Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Hongjie Liu ◽  
Xiao Fu ◽  
Liangping Qi
Keyword(s):  
Fixed Point ◽  
Green Function ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Existence Of Positive Solutions ◽  
Liouville Fractional Derivative ◽  
Fractional Boundary Value Problems

We are concerned with the following nonlinear three-point fractional boundary value problem:D0+αut+λatft,ut=0,0<t<1,u0=0, andu1=βuη, where1<α≤2,0<β<1,0<η<1,D0+αis the standard Riemann-Liouville fractional derivative,at>0is continuous for0≤t≤1, andf≥0is continuous on0,1×0,∞. By using Krasnoesel'skii's fixed-point theorem and the corresponding Green function, we obtain some results for the existence of positive solutions. At the end of this paper, we give an example to illustrate our main results.

Existence and asymptotical behavior of solutions for a quasilinear Choquard equation with singularity

2021 ◽  
Vol 19 (1) ◽  
pp. 259-267
Author(s):  
Liuyang Shao ◽  
Yingmin Wang
Keyword(s):  
Asymptotic Behavior ◽  
Positive Solutions ◽  
Riesz Potential ◽  
Asymptotic Behavior Of Solutions ◽  
Suitable Assumption ◽  
Choquard Equation ◽  
Existence Of Positive Solutions

Abstract In this study, we consider the following quasilinear Choquard equation with singularity − Δ u + V ( x ) u − u Δ u 2 + λ ( I α ∗ ∣ u ∣ p ) ∣ u ∣ p − 2 u = K ( x ) u − γ , x ∈ R N , u > 0 , x ∈ R N , \left\{\begin{array}{ll}-\Delta u+V\left(x)u-u\Delta {u}^{2}+\lambda \left({I}_{\alpha }\ast | u{| }^{p})| u{| }^{p-2}u=K\left(x){u}^{-\gamma },\hspace{1.0em}& x\in {{\mathbb{R}}}^{N},\\ u\gt 0,\hspace{1.0em}& x\in {{\mathbb{R}}}^{N},\end{array}\right. where I α {I}_{\alpha } is a Riesz potential, 0 < α < N 0\lt \alpha \lt N , and N + α N < p < N + α N − 2 \displaystyle \frac{N+\alpha }{N}\lt p\lt \displaystyle \frac{N+\alpha }{N-2} , with λ > 0 \lambda \gt 0 . Under suitable assumption on V V and K K , we research the existence of positive solutions of the equations. Furthermore, we obtain the asymptotic behavior of solutions as λ → 0 \lambda \to 0 .

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