A Note on nonautonomous klein-gordon-schrödinger equations with homogeneous dirichlet boundary condition

2008 ◽  
Vol 28 (4) ◽  
pp. 823-833 ◽  
Author(s):  
Zhao Caidi ◽  
Zhou Shengfan ◽  
Li Yongsheng
Keyword(s):  
Boundary Condition ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Homogeneous Dirichlet Boundary Condition ◽  
Klein Gordon

scholarly journals On some classes of generalized Schrödinger equations

2020 ◽  
Vol 10 (1) ◽  
pp. 522-533
Author(s):  
Amanda S. S. Correa Leão ◽  
Joelma Morbach ◽  
Andrelino V. Santos ◽  
João R. Santos Júnior
Keyword(s):  
Boundary Condition ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Laplacian Operator ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nontrivial Solutions ◽  
Homogeneous Dirichlet Boundary Condition ◽  
Stationary Problems

Abstract Some classes of generalized Schrödinger stationary problems are studied. Under appropriated conditions is proved the existence of at least 1 + $\begin{array}{} \sum_{i=2}^{m} \end{array}$ dim Vλi pairs of nontrivial solutions if a parameter involved in the equation is large enough, where Vλi denotes the eigenspace associated to the i-th eigenvalue λi of laplacian operator with homogeneous Dirichlet boundary condition.

scholarly journals A Lotka-Volterra Competition Model with Cross-Diffusion

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Wenyan Chen ◽  
Ya Chen
Keyword(s):  
Boundary Condition ◽  
Positive Solutions ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Upper And Lower Solutions ◽  
Sufficient Conditions ◽  
Competition Model ◽  
Homogeneous Dirichlet Boundary Condition ◽  
Cross Diffusion ◽  
Existence Of Positive Solutions

A Lotka-Volterra competition model with cross-diffusions under homogeneous Dirichlet boundary condition is considered, where cross-diffusions are included in such a way that the two species run away from each other because of the competition between them. Using the method of upper and lower solutions, sufficient conditions for the existence of positive solutions are provided when the cross-diffusions are sufficiently small. Furthermore, the investigation of nonexistence of positive solutions is also presented.

scholarly journals Dirichlet boundary condition for the Lee–Wick-like scalar model

2020 ◽  
Vol 80 (11) ◽  
Author(s):  
L. H. C. Borges ◽  
A. A. Nogueira ◽  
E. H. Rodrigues ◽  
F. A. Barone
Keyword(s):  
Boundary Condition ◽  
Scalar Field ◽  
Gauge Field ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Image Method ◽  
Scalar Model ◽  
Scalar Charge ◽  
Klein Gordon

AbstractLee–Wick-like scalar model near a Dirichlet plate is considered in this work. The modified propagator for the scalar field due to the presence of a Dirichlet boundary is computed, and the interaction between the plate and a point-like scalar charge is analysed. The non-validity of the image method is investigated and the results are compared with the corresponding ones obtained for the Lee–Wick gauge field and for the standard Klein–Gordon field.

scholarly journals Blow-up and energy decay for a class of wave equations with nonlocal Kirchhoff-type diffusion and weak damping

2021 ◽  
Author(s):  
Menglan Liao ◽  
Zhong Tan
Keyword(s):  
Boundary Condition ◽  
Differential Operator ◽  
Initial Data ◽  
Dirichlet Boundary Condition ◽  
Wave Equations ◽  
Dirichlet Boundary ◽  
Blow Up ◽  
Homogeneous Dirichlet Boundary Condition ◽  
Kirchhoff Type ◽  
Weak Damping

The purpose of this paper is to study the following equation driven by a nonlocal integro-differential operator $\mathcal{L}_K$: \[u_{tt}+[u]_s^{2(\theta-1)}\mathcal{L}_Ku+a|u_t|^{m-1}u_t=b|u|^{p-1}u\] with homogeneous Dirichlet boundary condition and initial data, where $[u]^2_s$ is the Gagliardo seminorm, $a\geq 0,~b>0,~0

On a family of torsional creep problems involving rapidly growing operators in divergence form

2018 ◽  
Vol 149 (2) ◽  
pp. 495-510 ◽  
Author(s):  
Maria Fărcăşeanu ◽  
Mihai Mihăilescu
Keyword(s):  
Boundary Condition ◽  
Uniform Convergence ◽  
Bounded Domain ◽  
Distance Function ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Smooth Boundary ◽  
Divergence Form ◽  
Homogeneous Dirichlet Boundary Condition ◽  
Real Numbers

Let Ω⊂ℝN (N≥2) be a bounded domain with smooth boundary and {pn} be a sequence of real numbers converging to+∞ as n→∞. For each integer n>1, we define the function $\varphi_{n}(t)=p_{n} \vert t \vert^{p_{n}-2}te^{ \vert t \vert^{p_{n}}}$, for all t∈ℝ, and we prove the existence of a unique nonnegative variational solution for the problem−div(((φn(|∇ u(x)|))/(|∇ u(x)|))∇ u(x))=φn(1), when x∈Ω, subject to the homogeneous Dirichlet boundary condition. Next, we establish the uniform convergence in Ω of the sequence of solutions for the above family of equations to the distance function to the boundary of Ω. Our result complements the earlier developments on the topic obtained by Payne and Philippin [26], Kawohl [21], Bhattacharya, DiBenedetto and Manfredi [2], Perez-Llanos and Rossi [27] and Bocea and Mihăilescu [4].

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