![]() ![]() Tarantello : A note on a semilinear elliptic problem. Micheletti AM, Pistoia A, Sacon A: Three solutions of a 4th order elliptic problem via variational theorems of mixed type. Micheletti AM, Pistoia A: Multiplicity results for a fourth-order semilinear elliptic problem. ![]() Nonlinear Analysis, Theory, Methods and Applications 1984, 8: 893–907. McKenna PJ, Walter W: On the multiplicity of the solution set of some nonlinear boundary value problems. Lazer AC, McKenna PJ: Large amplitude periodic oscillations in suspension bridges:, some new connections with nonlinear analysis. Lazer AC, McKenna PJ: Multiplicity results for a class of semilinear elliptic and parabolic boundary value problems. Jung T, Choi QH: On the existence of the third solution of the nonlinear biharmonic equation with Dirichlet boundary condition. Nonlinear Analysis, Theory, Methods and Applications 1997, 30(8):5083–5092. Jung TS, Choi QH: Multiplicity results on a nonlinear biharmonic equation. Acta Mathematica Scientia 1999, 19(4):361–374.Ĭhoi QH, Jung T: Multiplicity results on nonlinear biharmonic operator. By Lemma 3.2 and Lemma 3.3, we haveĬhoi QH, Jung T: Multiplicity of solutions and source terms in a fourth order nonlinear elliptic equation. In section 4, we prove Theorem 1.2 by using the contraction mapping principle.į ( w + σ e 1 ) ≥ 1 2 λ k + n + 1 ( λ k + n + 1 - c ) ∥ w ∥ L 2 ( Ω ) 2 + σ 2 2 ∥ e 1 ∥ 2 (1) - ∫ Ω d x (2) = 1 2. In section 3, we prove Theorem 1.1 by using the critical point theory and variation of linking method. In section 2 we define a Banach space H spanned by eigenfunctions of Δ 2 + c Δ with Dirichlet boundary condition and investigate some properties of system (1.1). Then system (1.1) has a unique nontrivial solution. Suppose that ab ≠ 0 and d e t 1 1 b - a ≠ 0. 1) has at least two nontrivial solutions. In this paper we improve the multiplicity results of the single fourth order elliptic problem to that of the fourth order elliptic system. In the authors investigate the existence of solutions of jumping problems with Dirichlet boundary condition. They also proved that when c < λ 1, λ 1( λ 1 - c) < b < λ 2( λ 2 - c) and s < 0, (1.3) has at least three solutions by using degree theory. They also obtained these results by using the variational reduction method. Remark that the exact solution reads: u ( x, y) sin ( k 0 x) sin ( k 0 y) This example is the Dirichlet boundary condition conterpart to this Dolfinx tutorial. The aim of this paper is to construct accurate absorbing boundary conditions (ABCs) suitable for classical (local) as well as nonlocal peridynamic (PD) diffusion models. Linear Liouville equations with discontinuous and even measure-valuedĬoefficients.They show that (1.3) has at least two nontrivial solutions when c 0. with the Dirichlet boundary conditions u ( x, y) 0, ( x, y) and a source term f ( x, y) k 0 2 sin ( k 0 x) sin ( k 0 y). Diffusion-type problems in (nearly) unbounded domains play important roles in various fields of fluid dynamics, biology, and materials science. Problems, we study the (parabolic) Stefan problem, linear convection, and Linear convection equation with inflow boundary conditions and the heatĮquation with Dirichlet and Neumann boundary conditions. We implement this method for several typical problems, including the So-called warped phase transformation that maps the equation into one higherĭimension. Non-Hermitian dynamics to a system of Schrödinger equations, via the 2022) - it converts any linear PDEs and ODEs with Issue can be resolved by using a recently introduced Schrödingerisation Semi-discretisation of such problems does not necessarily yield Hamiltonianĭynamics and even alters the Hamiltonian structure of the dynamics whenīoundary and interface conditions are included. Download a PDF of the paper titled Quantum Simulation for Partial Differential Equations with Physical Boundary or Interface Conditions, by Shi Jin and Xiantao Li and Nana Liu and Yue Yu Download PDF Abstract: This paper explores the feasibility of quantum simulation for partialĭifferential equations (PDEs) with physical boundary or interface conditions. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |