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 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 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}.

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