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1
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Nonlinear boundary value problems for differential inclusions y'' ∈ F(t,y,y')

100%
Erbe L., Krawcewicz W.
Annales Polonici Mathematici
|
1991
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tom 54
|
nr 3
195-226
EN
Applying the topological transversality method of Granas and the a priori bounds technique we prove some existence results for systems of differential inclusions of the form y'' ∈ F(t,y,y'), where F is a Carathéodory multifunction and y satisfies some nonlinear boundary conditions.
2
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The gradient projection method for solving an optimal control problem

100%
Farag M. H.
Applicationes Mathematicae
|
1996-1997
|
tom 24
|
nr 2
141-147
EN
A gradient method for solving an optimal control problem described by a parabolic equation is considered. The gradient projection method is applied to solve the problem. The convergence of the projection algorithm is investigated.
3
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Nontrivial critical points of asymptotically quadratic functions at resonances

100%
Fečkan M.
Annales Polonici Mathematici
|
1997
|
tom 67
|
nr 1
43-57
EN
Asymptotically quadratic functions defined on Hilbert spaces are studied by using some results of the theory of Morse-Conley index. Applications are given to existence of nontrivial weak solutions for asymptotically linear elliptic partial and ordinary differential equations at resonances.
4
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Existence of solutions for a multivalued boundary value problem with non-convex and unbounded right-hand side

88%
Averna D., Bonanno G.
Annales Polonici Mathematici
|
1999
|
tom 71
|
nr 3
253-271
EN
Let $F:[a,b] × ℝ^n × ℝ^n → 2^{ℝ^n}$ be a multifunction with possibly non-convex and unbounded values. The main result of this paper (Theorem 1) asserts that, given the multivalued boundary value problem ($P_F$)    {u'' ∈ F(t,u,u'),                    u(a) = u(b) = ϑ_{ℝ^n}, if an appropriate restriction of the multifunction F has non-empty and closed values and satisfies the lower Scorza Dragoni property and a weak integrable boundedness type condition, then we can substitute the problem ($P_F$) with another one ($P_G$), with a suitable convex right-hand side G, such that every generalized solution of ($P_G$) is also a generalized solution of ($P_F$) (see also Remark 1 and Corollary 1). As a consequence of our results, in conjunction with those in [13] and [18], some existence theorems for multivalued boundary value problems are then presented (see Theorem 2, Corollary 2 and Theorem 3). Finally, some applications are given to the existence of generalized solutions for two implicit boundary value problems (Theorems 4-6).
5
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Boundary value problems with continuous and special gluing conditions for parabolic-hyperbolic type equations

88%
Eshmatov B., Karimov E.
Open Mathematics
|
2007
|
tom 5
|
nr 4
741-750
EN
In the present paper we study the unique solvability of two non-local boundary value problems with continuous and special gluing conditions for parabolic-hyperbolic type equations. The uniqueness of the solutions of the considered problems are proven by the “abc” method. Existence theorems for the solutions of these problems are proven by the method of integral equations. The obtained results can be used for studying local and non-local boundary-value problems for mixed-hyperbolic type equations with two and three lines of changing type.
6
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Reconstruction of potential and boundary conditions for second order difference equations

88%
Currie S., Love A.
Commentationes Mathematicae
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2018
|
tom 58
|
nr 1-2
EN
Assume the eigenvalues and the weights are given for a difference boundary value problem and that the form of the boundary conditions at the endpoints is known. In particular, it is known whether the endpoints are fixed (i.e. Dirichlet or non-Dirichlet boundary conditions) or whether the endpoints are free to move (i.e. boundary conditions with affine dependence on the eigenparameter). This work illustrates how the potential as well as the exact boundary conditions can be uniquely reconstructed. The procedure is inductive on the number of unit intervals. This paper follows along the lines of S. Currie and A. Love, Inverse problems for difference equations with quadratic eigenparameter dependent boundary conditions, \emph{Quaestiones Mathematicae}, 40 (2017), no. 7, 861−877. Since the inverse problem considered in this paper contains more unknowns than the inverse problem considered in the above reference, an additional spectrum is required more often than was the case in the unique reconstruction of the potential alone.
7
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The Behaviour of Weak Solutions of Boundary Value Problems for Linear Elliptic Second Order Equations in Unbounded Cone-Like Domains

88%
Wiśniewski D.
Annales Mathematicae Silesianae
|
2016
|
tom 30
|
nr 1
203-217
EN
We investigate the behaviour of weak solutions of boundary value problems (Dirichlet, Neumann, Robin and mixed) for linear elliptic divergence second order equations in domains extending to infinity along a cone. We find an exponent of the solution decreasing rate: we derive the estimate of the weak solution modulus for our problems near the infinity under assumption that leading coefficients of the equations do not satisfy the Dini-continuity condition.
8
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Asymptotic of weak solutions for linear elliptic nonlocal Robin problem without Dini-continuity condition in a plane angle domain

75%
Żyjewski K.
Commentationes Mathematicae
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2017
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tom 57
|
nr 1
EN
We investigate the behaviour of weak solutions to the nonlocal Robin problem for linear elliptic divergence second order equations in a neighbourhood of the boundary corner point. We find the exponent of the solution decreasing rate under the assumption that the leading coefficients of the equations do not satisfy the Dini-continuity condition.
9
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The existence of solution for boundary value problems for differential equations with deviating arguments and p-Laplacian

75%
Liu B., Yu J.
Annales Polonici Mathematici
|
2000
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tom 75
|
nr 3
271-280
EN
We consider a boundary value problem for a differential equation with deviating arguments and p-Laplacian: $-(ϕ_{p}(x'))' + d/dt grad F(x) + g(t,x(t),x(δ(t))$, x'(t), x'(τ(t))) = 0, t ∈ [0,1]; $x(t)=\underline{φ}(t),$ t ≤ 0; $x(t) = \overline{φ}(t)$, t ≥ 1. An existence result is obtained with the help of the Leray-Schauder degree theory, with no restriction on the damping forces d/dt grad F(x).
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