共查询到20条相似文献,搜索用时 15 毫秒
1.
Three important inequalities (the Poincaré, Hardy and generalized Poincaré inequalities) on the mixed boundary conditions are firstly established by some analytical techniques. Then the existence and multiplicity of positive solutions are studied for a class of semilinear elliptic equations with mixed Dirichlet-Neumann boundary conditions involving Hardy terms and Hardy-Sobolev critical exponents by using the variational methods. 相似文献
2.
The purpose of this paper is an extension of Jacobi’s criteria for positive definiteness of second variation of the simplest problems of calculus of variations subject to mixed boundary conditions. Both non constrained and isoperimetric problems are discussed. The main result is that if we stipulate conditions (21) and (22) then Jacobi’s condition remains valid also for the mixed boundary conditions. 相似文献
3.
利用混合单调算子不动点定理研究了一维非线性奇异P-Lapace差分方程边值问题,得到P-Lapace差分方程边值问题的存在唯一正解的充要条件. 相似文献
4.
利用不动点指数理论,研究了Banach空间中一类带奇性的混合型积分——微分方程边值问题正解的存在性,得到了多个正解存在的充分条件,并给出了相应的例子以说明所得结果的合理性和应用性. 相似文献
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7.
The existence and multiplicity of positive solutions are studied for a class of quasilinear elliptic equations involving Sobolev critical exponents with mixed Dirichlet-Neumann boundary conditions by the variational methods and some analytical techniques. 相似文献
8.
Curtis J. Kunkel 《Journal of Difference Equations and Applications》2013,19(4):411-420
We study singular discrete second order boundary value problems with mixed boundary conditions over a finite interval. We prove the existence of a positive solution by means of the lower and upper solutions method and the Brouwer fixed point theorem in conjunction with perturbation methods to approximate regular problems. 相似文献
9.
By fixed point theorem of a mixed monotone operators, we study Lidstone boundary value problems to nonlinear singular 2mth-order differential and difference equations, and provide sufficient conditions for the existence and uniqueness of positive solution to Lidstone boundary value problem for 2mth-order ordinary differential equations and 2mth-order difference equations. The nonlinear term in the differential and difference equation may be singular. 相似文献
10.
Ansgar Jüngel 《Mathematische Nachrichten》1997,185(1):85-110
A multi-dimensional transient drift-diffusion model for (at most) three charged particles, consisting of the continuity equations for the concentrations of the species and the Poisson equation for the electric potential, is considered. The diffusion terms depend on the concentrations. Such a system arises in electrophoretic modeling of three species (neutrally, positively and negatively charged) and in semiconductor theory for two species (positively charged holes and negatively charged electrons). Diffusion terms of degenerate type are also possible in semiconductor modeling. For the initial boundary value problem with mixed Dirichlet - Neumann boundary conditions and general reaction rates, a global existence result is proved. Uniqueness of solutions follows in the Dirichlet boundary case if the diffusion terms are uniformly parabolic or if the initial and boundary densities are strictly positive. Finally, we prove that solutions exist which are positive uniformly in time and globally bounded if the reaction rates satisfy appropriate growth conditions. 相似文献
11.
A variational inequality approach to generalized two-phase Stefan problem in several space variables 总被引:1,自引:0,他引:1
Irena Pawłow 《Annali di Matematica Pura ed Applicata》1982,131(1):333-373
Summary The paper offers a study of a broad class of multidimensional two- phase problems of Stefan type by means of variational inequality techniques. The problems for quasilinear equations of alternatively parabolic or mixed parabolicelliptic type, mixed type nonlinear conditions at the fixed lateral boundary, involving free boundary conditions corresponding to phase transitions of both first (latent heat positive) and second kind (latent heat equal to zero) are taken into consideration. Results concerning existence of weak solutions, their uniqueness and stability are established.The preparation of the paper was partially carried out while the author's visiting Istituto di Analisi Numerica del C.N.R., Pavia, due to support of the C.N.R. 相似文献
12.
In this paper we consider boundary value problems in perforated domains with periodic structures and cavities of different scales, with the Neumann condition on some of them and mixed boundary conditions on others. We take a case when cavities with mixed boundary conditions have so called critical size (see [1]) and cavities with the Neumann conditions have the scale of the cell. In the same way other cases can be studied, when we have the Neumann and the Dirichlet boundary conditions or the Dirichlet condition and the mixed boundary condition on the boundary of cavities.There is a large literature where homogenization problems in perforated domains were studied [2];-[7]; 相似文献
13.
B. C. Dhage 《Applicable analysis》2013,92(2):205-221
In this article, the authors prove an existence theorem for periodic boundary value problems for first order functional differential equations (FDE) in Banach algebras under mixed generalized Lipschitz and Carathéodory conditions. The existence of extremal positive solutions is also proved under certain monotonicity conditions. An example illustrating the results is included. 相似文献
14.
讨论了一类具有混合单调非线性项的四阶微分方程两点边值问题,运用一类混合单调算子的不动点定理及"和型"非线性算子的不动点定理,结合单调迭代技巧和格林函数的性质,获得方程正解存在且唯一的充分条件,并构造两个迭代序列收敛于此唯一解.最后,给出具体的例子验证了定理的正确性. 相似文献
15.
In this paper we prove the nonexistence of positive solutions of the equation-Δu=u2*-1 inR
+
N
with certain homogeneous mixed boundary conditions. The proof is based on a monotonicity theorem obtained using the moving
plane methods and some recent results of Berestycki and Nirenberg (see [BN]). The nonexistence theorem is applied to improve
a result of [GP] on the characterization of the critical levels of a functional related to some nonlinear elliptic problem
with critical Sobolev exponent and mixed boundary conditions. 相似文献
16.
Wesley E. Brittin 《Applicable analysis》2013,92(4):245-260
Unitary operators are introduced which act on the Fourier transforms of the boundary values on concentric cylinders of a harmonic function in E 3. The boundary values on the concentric cylinders are determined from given mixed boundary conditions on the same cylinders, and the solution for them is expressed explicitly and simply through the use of these unitary operators plus certain other self adjoint positive operators. The boundary values on the cylinders then determine the harmonic function everywhere in E 3. 相似文献
17.
E. A. Gasymov A. O. Guseinova U. N. Gasanova 《Computational Mathematics and Mathematical Physics》2016,56(7):1305-1309
One of the methods for solving mixed problems is the classical separation of variables (the Fourier method). If the boundary conditions of the mixed problem are irregular, this method, generally speaking, is not applicable. In the present paper, a generalized separation of variables and a way of application of this method to solving some mixed problems with irregular boundary conditions are proposed. Analytical representation of the solution to this irregular mixed problem is obtained. 相似文献
18.
In this paper, we deal with a diffusive predator-prey model with mixed boundary conditions, in which the prey population can escape from the boundary of the domain while predator population can only live in this area and can not leave. We first investigate the asymptotic behaviour of positive solutions and obtain a necessary condition ensuring the existence of positive steady state solutions. Next, we investigate the existence of positive steady state solutions by using maximum principle, the fixed point index theory, Lpestimation, and embedding theorems, Finally, local stability and uniqueness are obtained by linear stability theory and perturbation theory of linear operators. 相似文献
19.
In this article we present a new fixed point theorem for a class of general mixed monotone operators, which extends the existing corresponding results. Moreover, we establish some pleasant properties of nonlinear eigenvalue problems for mixed monotone operators. Based on them the local existence-uniqueness of positive solutions for nonlinear boundary value problems which include Neumann boundary value problems, three-point boundary value problems and elliptic boundary value problems for Lane-Emden-Fowler equations is proved. The theorems for nonlinear boundary value problems obtained here are very general. 相似文献
20.
We consider extremal problems for the time-harmonic Maxwell equations with mixed boundary conditions for the electric field. Namely, the tangential component of the electric field is given on one part of the boundary, and an impedance boundary condition is posed on the other part. We prove the solvability of the original mixed boundary value problem and the extremal problem. We obtain sufficient conditions on the input data ensuring the stability of solutions of specific extremal problems under certain perturbations of both the performance functional and some functions occurring in the boundary value problem. 相似文献