Dirichlet problem
Dirichlet problem in Banach spaces: the bound sets approach
... The main aim of our present paper is an extension of the finite-dimensional results in [, ] into infinite-dimensional ones. We were also stimulated by the work of Jean Mawhin in [], where degree arguments were applied ...
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Scorza-Dragoni approach to Dirichlet problem in Banach spaces
... Hartman-type conditions are presented for the solvability of a multivalued Dirichlet problem in a Banach space by means of topological degree arguments, bounding functions, and a Scorza-Dragoni ...
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The Dirichlet Problem for the Equation in the Exterior of Nonclosed Lipschitz Surfaces
... the Dirichlet problem for the equation Δ𝑢 − 𝑘 2 𝑢 = 0 in the exterior of nonclosed Lipschitz surfaces in 𝑅 3 ...The Dirichlet problem for the Laplace equation is a particular case of our ...
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Approximation on the hexagonal grid of the Dirichlet problem for Laplace’s equation
... grid functions. It is applied to construct a fourth order accurate interpolating function, on the closed rectangle, for the numerical solution of Laplace’s equation on the hexagonal grids. Further, the matching operator ...
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Fredholm alternative for the second-order singular Dirichlet problem
... has no nontrivial solution satisfying (). The above statement plays an important role in the theory of singular problems; however, it does not cover many interesting, even rather simple, equations. For example, consider ...
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A remark on the Dirichlet problem in a half plane
... 6. Qiao, L: Integral representations for harmonic functions of infinite order in a cone. Results Math. 61(3), 63-74 (2012) 7. Qiao, L, Pan, GS: Integral representations of generalized harmonic functions. Taiwan. J. Math. ...
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The Dirichlet problem for the time-fractional advection-diffusion equation in a line segment
... The one-dimensional time-fractional advection-diffusion equation with the Caputo time derivative is considered in a line segment. The fundamental solution to the Dirichlet problem and the solution of the ...
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On a generalization of the Dirichlet problem for the Poisson equation
... In this paper, we investigate a generalization of the Dirichlet problem for the Poisson equation in a rectangular domain. We assume that the kth-order normal derivatives of an unknown function are given on ...
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Uniqueness results for the Dirichlet problem for higher order elliptic equations in polyhedral angles
... Successively, many authors studied analogous problems in more general cases and with different methods (see, for instance, [–], the general survey on this subject [] and the references quoted therein). In particular, ...
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Ground state solutions of Kirchhoff type fractional Dirichlet problem with p Laplacian
... Ground state solutions of Kirchhoff type fractional Dirichlet problem with p Laplacian Chen and Liu Advances in Difference Equations (2018) 2018 436 https //doi org/10 1186/s13662 018 1902 6 R E S E A[.] ...
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The Dirichlet problem for the Laplace equation in supershaped annuli
... The Dirichlet problem for the Laplace equation in normal-polar annuli is addressed by using a suitable Fourier-like technique. Attention is in particular focused on the wide class of domains whose ...
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Dirichlet problem for the Schrödinger operator on a cone
... the Dirichlet problem for the Schrödinger operator on a cone is constructed by the generalized Poisson integral with a slowly growing continuous boundary ...
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Dirichlet problem for divergence form elliptic equations with discontinuous coefficients
... the Dirichlet problem for linear elliptic second order partial differential equations with discontinuous coefficients in divergence form in unbounded ...
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Mathematical approach and numerical analysis to the fundamental solutions method of Dirichlet problem
... 1. Introduction. The fundamental solutions method (or charge simulation method) has been applied to the problem in electrical engineering, numerical conformal map- pings [2, 9] and Dirichlet problems [12, ...
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The exact asymptotic behaviour of the unique solution to a singular Dirichlet problem
... − Δ u ≥ f (x,u), u > 0, x ∈ Ω, u | ∂Ω = 0. (4.3) Lemma 4.3 [5, Lemma 3]. Let f (x, s) be locally H¨older continuous in Ω × (0, ∞ ) and con- tinuously differentiable with respect to the variable s. Suppose ...
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Nontrivial solution for asymmetric (p,2)-Laplacian Dirichlet problem
... the (AR)-condition in the positive semi-axis. In fact, this condition was studied by Liu and Wang in [] in the case of Laplacian (i.e., p = ) by the Nehari manifold approach. How- ever, we will use the mountain pass ...
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Fredholm’s third theorem for second-order singular Dirichlet problem
... We will need the next lemma in the proof of the sufficiency part of Theorem . and thus, we will suppose that Theorem . and the necessity part of Theorem . are true. Lemma . Let () hold and the homogeneous ...
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To a nonlocal generalization of the Dirichlet problem
... mixed problem with a boundary Dirichlet condition and non- local integral condition is considered in a unit square for a second-order elliptic ...this problem in the weighted Sobolev space W ...
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On a Perturbed Dirichlet Problem for a Nonlocal Differential Equation of Kirchhoff Type
... The case λ 0 was considered in 3 and 4, where the existence of at least one positive solution is established under various hypotheses on f . In particular, in 3 the nonlinearity f is supposed to satisfy the well-known ...
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The Dirichlet problem for a class of nonlinear degenerate parabolic equations
... We study the first boundary value problem for a class of nonlinear degenerate parabolic equations − ∂u/∂t = div( A( ∇ u)). We first consider its regularized problem and establish some estimates. Based on ...
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