Multiplicity results for a class of singular elliptic equation involving sublinear Neumann boundary condition in $$\mathbb {R}^2$$ R 2

2017 ◽  
Vol 19 (4) ◽  
pp. 2963-2984 ◽  
Author(s):  
K. Saoudi
Keyword(s):  
Boundary Condition ◽  
Elliptic Equation ◽  
Neumann Boundary Condition ◽  
Neumann Boundary ◽  
Multiplicity Results ◽  
Singular Elliptic Equation

scholarly journals EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR A NEUMANN PROBLEM INVOLVING VARIABLE EXPONENT GROWTH CONDITIONS

2008 ◽  
Vol 50 (3) ◽  
pp. 565-574 ◽  
Author(s):  
MARIA-MAGDALENA BOUREANU ◽  
MIHAI MIHĂILESCU
Keyword(s):  
Boundary Condition ◽  
Elliptic Equation ◽  
Neumann Problem ◽  
Neumann Boundary Condition ◽  
Variable Exponent ◽  
Main Tool ◽  
Neumann Boundary ◽  
Growth Conditions ◽  
Linear Elliptic Equation ◽  
Existence And Multiplicity

AbstractIn this paper we study a non-linear elliptic equation involving p(x)-growth conditions and satisfying a Neumann boundary condition on a bounded domain. For that equation we establish the existence of two solutions using as a main tool an abstract linking argument due to Brézis and Nirenberg.

New solutions for critical Neumann problems in ℝ2

2017 ◽  
Vol 8 (1) ◽  
pp. 615-644
Author(s):  
Shengbing Deng ◽  
Monica Musso
Keyword(s):  
Boundary Condition ◽  
Elliptic Equation ◽  
Small Parameter ◽  
Neumann Boundary Condition ◽  
Neumann Boundary ◽  
Normal Vector ◽  
Bounded Smooth Domain ◽  
Neumann Problems ◽  
Bounded Smooth ◽  
Outer Normal Vector

Abstract We consider the elliptic equation {-\Delta u+u=0} in a bounded, smooth domain Ω in {\mathbb{R}^{2}} subject to the nonlinear Neumann boundary condition {\frac{\partial u}{\partial\nu}=\lambda ue^{u^{2}}} , where ν denotes the outer normal vector of {\partial\Omega} . Here {\lambda>0} is a small parameter. For any λ small we construct positive solutions concentrating, as {\lambda\to 0} , around points of the boundary of Ω.

scholarly journals Boundary unique continuation theorems under zero Neumann boundary conditions

2005 ◽  
Vol 72 (1) ◽  
pp. 67-85 ◽  
Author(s):  
Xiangxing Tao ◽  
Songyan Zhang
Keyword(s):  
Boundary Condition ◽  
Elliptic Equation ◽  
Boundary Conditions ◽  
Neumann Boundary Condition ◽  
Unique Continuation ◽  
Neumann Boundary ◽  
Lipschitz Domains ◽  
Singular Potentials ◽  
Order Elliptic Equation ◽  
Second Order Elliptic Equation

Let u be a solution to a second order elliptic equation with singular potentials belonging to the Kato-Fefferman-Phong's class in Lipschitz domains. We prove the boundary unique continuation theorems and the doubling properties for u2 near the boundary under the zero Neumann boundary condition.

scholarly journals Multiplicity Results for thepx-Laplacian Equation with Singular Nonlinearities and Nonlinear Neumann Boundary Condition

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
K. Saoudi ◽  
M. Kratou ◽  
S. Alsadhan
Keyword(s):  
Boundary Condition ◽  
Neumann Problem ◽  
Bounded Domain ◽  
Neumann Boundary Condition ◽  
Neumann Boundary ◽  
Positive Parameter ◽  
Multiplicity Results ◽  
Laplacian Equation ◽  
Variational Techniques ◽  
Singular Nonlinearities

We investigate the singular Neumann problem involving thep(x)-Laplace operator:Pλ{-Δpxu+|u|px-2u  =1/uδx+fx,u, in  Ω;  u>0,  in  Ω;  ∇upx-2∂u/∂ν=λuqx,  on  ∂Ω}, whereΩ⊂RNN≥2is a bounded domain withC2boundary,λis a positive parameter, andpx,qx,δx, andfx,uare assumed to satisfy assumptions(H0)–(H5)in the Introduction. Using some variational techniques, we show the existence of a numberΛ∈0,∞such that problemPλhas two solutions forλ∈0,Λ,one solution forλ=Λ, and no solutions forλ>Λ.

Inverse spectral problem of an anharmonic oscillator on a half-axis with the Neumann boundary condition

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Agil K. Khanmamedov ◽  
Nigar F. Gafarova
Keyword(s):  
Boundary Condition ◽  
Neumann Boundary Condition ◽  
Inverse Spectral Problem ◽  
Anharmonic Oscillator ◽  
Neumann Boundary ◽  
Effective Algorithm ◽  
Inverse Spectral Problems ◽  
Main Equation ◽  
Inverse Spectral ◽  
Half Axis

AbstractAn anharmonic oscillator {T(q)=-\frac{d^{2}}{dx^{2}}+x^{2}+q(x)} on the half-axis {0\leq x<\infty} with the Neumann boundary condition is considered. By means of transformation operators, the direct and inverse spectral problems are studied. We obtain the main integral equations of the inverse problem and prove that the main equation is uniquely solvable. An effective algorithm for reconstruction of perturbed potential is indicated.

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