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1
Content available remote On second order nonlocal boundary value problem at resonance
Szymańska-Dębowska K.
Fasciculi Mathematici
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2016
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Nr 56
143--153
EN
This work is devoted to the existence of solutions for a system of nonlocal resonant boundary value problem x''=f(t,x), x' (0)=0, x' (1)-∫1 0 x(s)dg(s), where f ∶ [0,1] × Rk → Rk is continuous and g ∶ [0,1] → Rk is a function of bounded variation.
2
Content available On a singular nonlinear Neumann problem
Chabrowski J.
Opuscula Mathematica
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2014
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Vol. 34, no. 2
271--290
EN
We investigate the solvability of the Neumann problem involving two critical exponents: Sobolev and Hardy-Sobolev. We establish the existence of a solution in three cases: (i) 2 < p+1 <2*s, (ii) p+1 = 2*(s) and (iii) 2*(s) < p+1 ≤ 2*, where [formula] denote the critical Hardy-Sobolev exponent and the critical Sobolev exponent, respectively.
3
Content available Constant-sign solutions for a nonlinear Neumann problem involving the discrete p-Laplacian
Candito P., D'Agui G.
Opuscula Mathematica
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2014
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Vol. 34, no. 4
683--690
EN
In this paper, we investigate the existence of constant-sign solutions for a nonlinear Neumann boundary value problem involving the discrete p-Laplacian. Our approach is based on an abstract local minimum theorem and truncation techniques.
4
Content available On elliptic problems with a nonlinearity depending on the gradient
Chabrowski J.
Opuscula Mathematica
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2009
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Vol. 29, no. 4
377-391
EN
We investigate the solvability of the Neumann problem (1.1) involving the non-linearity depending on the gradient. We prove the existence of a solution when the right hand side ƒ of the equation belongs to Lm( Ω) with 1 ≤m <2.
5
Content available remote Shape differentiability of the Neumann problem of the Laplace equation in the half-space
Amrouche C., Necasova S., Sokołowski J.
Control and Cybernetics
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2008
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Vol. 37, no 4
747-769
EN
We deal with the existence of the material derivative of the Laplace equation with the Neumann boundary condition in the half space. We consider two different perturbations of domains to get the existence of weak Gateaux material derivative and the existence of Fréchet material derivatives.
6
Content available remote Hemivariational inequalities governed by the p-Laplacian - Neumann problem
Naniewicz Z.
Control and Cybernetics
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2007
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Vol. 36, no 3
727-754
EN
A hemivariational inequality involving p-Laplacian is studied under the hypothesis that the nonlinear part fulfills the unilateral growth condition. The existence of solutions for problems with Neumann boundary conditions is established by making use of Chang's version of the critical point theory for nonsmooth locally Lipschitz functionals, combined with the Galerkin method. The approach is based on the recession technique introduced previously by the author.
7
Content available remote The interior Neumann problem for the Stokes resolvent system in a bounded domain in Rn
Kohr M.
Archives of Mechanics
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2007
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Vol. 59, nr 3
283-304
EN
The interior Neumann problem for the Stokes resolvent system is studied from the point of view of the potential theory. The existence and uniqueness results as well as boundary integral representations of the classical solution are given in the case of a bounded domain in Rn, having a compact but not connected boundary of class C1'" (0
8
Content available remote Indefinite quasilinear Neumann problem on unbounded domains
Chabrowski J.
Bulletin of the Polish Academy of Sciences. Mathematics
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2006
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Vol. 54, no 3-4
207-217
EN
We investigate the solvability of the quasilinear Neumann problem (1.1) with sub- and supercritical exponents in an unbounded domain Ω. Under some integrability conditions on the coefficients we establish embedding theorems of weighted Sobolev spaces into weighted Lebesgue spaces. This is used to obtain solutions through a global minimization of a variational functional.
9
Content available remote On the nonlinear Neumann problem with indefinite weight and Sobolev critical nonlinearity
Chabrowski J.
Bulletin of the Polish Academy of Sciences. Mathematics
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2002
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Vol. 50, no 3
323-333
EN
We prove the existence of positive solutions of the Neumann problem with indefinite weight and critical Sobolev nonlinearity. Our approach is based on the concentration-compactness principle applied to a related variational problem.
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