On the Eigenvalues of the Laplace Operator on a Thin Set with Neumann Boundary Conditions

1996 ◽  
Vol 61 (3-4) ◽  
pp. 293-306 ◽  
Author(s):  
Michelle Schatzman
Keyword(s):  
Boundary Conditions ◽  
Laplace Operator ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Thin Set ◽  
The Laplace Operator

scholarly journals Infinitely many solutions for mixed Dirichlet-Neumann problems driven by the (p,q)-laplace operator

Filomat ◽  
2019 ◽  
Vol 33 (14) ◽  
pp. 4603-4611 ◽  
Author(s):  
Francesca Vetro
Keyword(s):  
Boundary Conditions ◽  
Laplace Operator ◽  
Nonlinear Problem ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Infinitely Many Solutions ◽  
Neumann Problems ◽  
Reaction Term ◽  
Variational Tools

We study a nonlinear problem with mixed Dirichlet-Neumann boundary conditions involving the p-Laplace operator and the q-Laplace operator ((p,q)-Laplace operator). Using variational tools and appropriate hypotheses on the behavior either at infinity or at zero of the reaction term, we prove that such a problem has infinitely many solutions.

scholarly journals Dirichlet and Neumann boundary conditions for the p-Laplace operator: what is in between?

2012 ◽  
Vol 142 (5) ◽  
pp. 975-1002 ◽  
Author(s):  
Ralph Chill ◽  
Mahamadi Warma
Keyword(s):  
Boundary Conditions ◽  
Bounded Domain ◽  
Laplace Operator ◽  
Lower Semicontinuous ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Lipschitz Continuous ◽  
Type Boundary ◽  
Continuous Boundary

Let p ∈ (1, ∞) and let Ω ⊆ ℝN be a bounded domain with Lipschitz continuous boundary. We characterize on L2(Ω) all order-preserving semigroups that are generated by convex, lower semicontinuous, local functionals and are sandwiched between the semigroups generated by the p-Laplace operator with Dirichlet and Neumann boundary conditions. We show that every such semigroup is generated by the p-Laplace operator with Robin-type boundary conditions.

Corrigendum to: Dirichlet and Neumann boundary conditions for the p-Laplace operator: What is in between?

2019 ◽  
Vol 149 (6) ◽  
pp. 1689-1691
Author(s):  
Ralph Chill ◽  
Mahamadi Warma
Keyword(s):  
Boundary Conditions ◽  
Laplace Operator ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Original Proof

The implication $(i)\Rightarrow (ii)$ of Theorem 2.1 in our article [1] is not true as it stands. We give here two correct statements which follow from the original proof.

scholarly journals Onp→(x)-Anisotropic Problems with Neumann Boundary Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Anass Ourraoui
Keyword(s):  
Variational Method ◽  
Boundary Conditions ◽  
Laplace Operator ◽  
Nontrivial Solution ◽  
General Class ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Anisotropic Problems

This work is devoted to the study of a general class of anisotropic problems involvingp→(·)-Laplace operator. Based on the variational method, we establish the existence of a nontrivial solution without Ambrosetti-Rabinowitz type conditions.

scholarly journals Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions

2020 ◽  
Vol 18 (1) ◽  
pp. 1552-1564
Author(s):  
Huimin Tian ◽  
Lingling Zhang
Keyword(s):  
Boundary Conditions ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Neumann Boundary Conditions ◽  
Reaction Diffusion Equations ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Nonlocal Reaction

Abstract In this paper, the blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients are investigated under Neumann boundary conditions. By constructing some suitable auxiliary functions and using differential inequality techniques, we show some sufficient conditions to ensure that the solution u ( x , t ) u(x,t) blows up at a finite time under appropriate measure sense. Furthermore, an upper and a lower bound on blow-up time are derived under some appropriate assumptions. At last, two examples are presented to illustrate the application of our main results.

Recovering differential operators with two constant delays under Dirichlet/Neumann boundary conditions

2020 ◽  
Vol 28 (2) ◽  
pp. 237-241
Author(s):  
Biljana M. Vojvodic ◽  
Vladimir M. Vladicic
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Differential Operators ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions

AbstractThis paper deals with non-self-adjoint differential operators with two constant delays generated by {-y^{\prime\prime}+q_{1}(x)y(x-\tau_{1})+(-1)^{i}q_{2}(x)y(x-\tau_{2})}, where {\frac{\pi}{3}\leq\tau_{2}<\frac{\pi}{2}<2\tau_{2}\leq\tau_{1}<\pi} and potentials {q_{j}} are real-valued functions, {q_{j}\in L^{2}[0,\pi]}. We will prove that the delays and the potentials are uniquely determined from the spectra of four boundary value problems: two of them under boundary conditions {y(0)=y(\pi)=0} and the remaining two under boundary conditions {y(0)=y^{\prime}(\pi)=0}.

scholarly journals Numerical Solution of Nonlinear Schrödinger Equation with Neumann Boundary Conditions Using Quintic B-Spline Galerkin Method

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 469 ◽  
Author(s):  
Azhar Iqbal ◽  
Nur Nadiah Abd Hamid ◽  
Ahmad Izani Md. Ismail
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Spline Method ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
B Spline

This paper is concerned with the numerical solution of the nonlinear Schrödinger (NLS) equation with Neumann boundary conditions by quintic B-spline Galerkin finite element method as the shape and weight functions over the finite domain. The Galerkin B-spline method is more efficient and simpler than the general Galerkin finite element method. For the Galerkin B-spline method, the Crank Nicolson and finite difference schemes are applied for nodal parameters and for time integration. Two numerical problems are discussed to demonstrate the accuracy and feasibility of the proposed method. The error norms L 2 , L ∞ and conservation laws I 1 ,   I 2 are calculated to check the accuracy and feasibility of the method. The results of the scheme are compared with previously obtained approximate solutions and are found to be in good agreement.

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