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1.
Translated from Matematicheskie Zametki, Vol. 48, No. 2, pp. 10–18, August, 1990.  相似文献   

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For a differential-difference equation of the second order on the interval [0, d], we study the existence of a classical solution for arbitrary continuous right-hand sides. We show that a necessary and sufficient condition for the existence of a classical solution of the problem in the case where there exists a generalized solution is the absence of argument shifts in the derivatives of the unknown function occurring in the equation.  相似文献   

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This paper investigates the maximal and minimal solutions of periodic boundary value problems for first order nonlinear integro-differential equations of mixed type by establishing a comparison result and using the monotone iterative technique.  相似文献   

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We study an elliptic-parabolic problem appearing in the theory of partially saturated flows in the framework of viscosity solutions. This is part of current investigation to understand the theory of viscosity solutions for PDE problems involving free boundaries. We prove that the problem is well posed in the viscosity setting and compare the results with the weak theory. Dirichlet or Neumann boundary conditions are considered.  相似文献   

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In this paper, we study the existence of multiple solutions for boundary value problems of second-order difference equations with resonance at both infinity and zero by using Morse theory, critical point theory, minimax methods and bifurcation theory.  相似文献   

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Summary We investigate the homogeneous Dirichlet problem in H2,p for a second order elliptic partial differential equation in nondivergence form Lu=f in the case in which the leading coefficients of L belong to H1,n(), Rn. We prove that if p belongs to a suitable neighbourhood of 2, then the above problem, has a unique solution u satisfying D2up Cfp; furthermore, if f Hk,p, k=1,2, ..., and the coefficients of L satisfy some natural conditions, then the solution satisfies .Lavoro eseguito nell'ambito del gruppi 40% e 60% del M.P.I.  相似文献   

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We discuss the existence of minimal and maximal solutions for a class of first order nonlinear impulsive functional integro-differential equations of mixed type with anti-periodic boundary conditions. The main tool of study is the monotone iterative technique.  相似文献   

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Shooting methods are employed to obtain solutions of the three-point boundary value problem for the second order equation, where is continuous, and and conditions are imposed implying that solutions of such problems are unique, when they exist.

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14.
We consider boundary value problems of the first and third kind for the diffusionwave equation. By using the method of energy inequalities, we find a priori estimates for the solutions of these boundary value problems.  相似文献   

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In this paper we study the existence of positive solutions of the equation
(φ(x))+a(t)f(x(t))=0,  相似文献   

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Summary Recently, Galerkin and collocation methods have been analyzed for boundary integral equation formulations of some potential problems in the plane with nonlinear boundary conditions, and stability results and error estimates in theH 1/2-norm have been proved (Ruotsalainen and Wendland, and Ruotsalainen and Saranen). We show that these results extend toL p setting without any extra conditions. These extensions are proved by studying the uniform boundedness of the inverses of the linearized integral operators, and then considering the nonlinear equations. The fact that inH 1/2 setting the nonlinear operator is a homeomorphism with Lipschitz continuous inverse plays a crucial role. Optimal error estimates for the Galerkin and collocation method inL p space then follow.This research was performed while the second author was visiting professor at the University of Delaware, spring 1989  相似文献   

18.
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   

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We employ the critical point theory to establish the existence of nontrivial solutions for some boundary value problems of second-order difference equations.  相似文献   

20.
The paper studies the problem of existence of positive solution to the following boundary value problem: $D_{0^ + }^\sigma u''(t) - g(t)f(u(t)) = 0$ , t ∈ (0, 1), u″(0) = u″(1) = 0, au(0) ? bu′(0) = Σ i=1 m?2 a i u i ), cu(1) + du′(1) = Σ i=1 m?2 b i u(ξ i ), where $D_{0^ + }^\sigma$ is the Riemann-Liouville fractional derivative of order 1 < σ ≤ 2 and f is a lower semi-continuous function. Using Krasnoselskii’s fixed point theorems in a cone, the existence of one positive solution and multiple positive solutions for nonlinear singular boundary value problems is established.  相似文献   

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