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Stabilization of nonlocal solitons by boundary conditions
Optics Letters, 2014We discovered that boundary conditions can stabilize nonlocal solitons with an oscillatory periodic response function. These solitons are the equivalent of quadratic solitons consisting of fundamental waves and oscillatory second harmonics, which are unstable unless subject to boundary confinement.
Jing, Wang, Yiheng, Li, Qi, Guo, Wei, Hu
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Nonlocal Fractional Boundary Value Problems with Slit-Strips Boundary Conditions
Fractional Calculus and Applied Analysis, 2015In this paper, nonlocal boundary value problems of fractional differential equations and inclusions with slit-strips integral boundary conditions are investigated. Precisely, the existence and uniqueness of the solution for the single valued case is proved and the existence of solutions for the multivalued case is established. One of the main tool with
Ahmad, Bashir, Ntouyas, Sotiris K.
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Gellerstedt Problem with a Nonlocal Parity Boundary Condition
Lobachevskii Journal of Mathematics, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Electrical Conductivity Reconstruction Using Nonlocal Boundary Conditions
SIAM Journal on Applied Mathematics, 1999Summary: We study existence, uniqueness, and solution estimates to the mixed problem \(\nabla\cdot\sigma\nabla u=0\) with Dirichlet to Neumann map boundary conditions and Neumann boundary conditions. We then show how this can be used in the reconstruction of \(\sigma\), given the relationship between u and its normal derivative on the boundary portion ...
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(Super)Critical nonlocal equations with periodic boundary conditions
Selecta Mathematica, 2018In this paper the authors discuss the existence and multiplicity of periodic solutions for a class of parametric nonlocal equations with critical and supercritical growth. More specifically, given \(s\in (0,1)\), \(N>2s\), \(m>0\), the authors investigate the existence and multiplicity of periodic solutions for the class of problems \[ ((-\Delta+m^2)^s)
Ambrosio V., Mawhin J., Molica Bisci G
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On Fractional Differential Inclusions with Nonlocal Boundary Conditions
Fractional Calculus and Applied Analysis, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Castaing, Charles +3 more
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Differential operators with nonlocal boundary conditions
Differential Equations, 2000Inverse problems of spectral analysis are studied for boundary value problems generated by the Sturm-Liouville differential operator \[ \ell y:=y''+q(x)y, \quad ...
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On a Nonlocal BVP with Nonlinear Boundary Conditions
Results in Mathematics, 2012The author considers the existence of a positive solution to a boundary value problem where one of the boundary conditions is allowed to be nonlocal and nonlinear, namely \[ \begin{gathered} u''(t)+f(t,u(t))=0,\;t \in (0,1),\\ u(0) =H_{1}(\varphi (u))+\int_E H_{2}(s,u(s))\,ds,\;u(1) =0.\\ \end{gathered} \] Here, \(E\) is a measurable subset of \((0,1)\)
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Third order boundary value problems with nonlocal boundary conditions
Nonlinear Analysis: Theory, Methods & Applications, 2009The authors consider third order boundary value problems for nonlinear ordinary differential equations with nonlocal linear boundary conditions given by Stieltjes integrals. Conditions for the existence of multiple positive solutions are studied. Fixed point considerations in cones and index theory are employed. Two illustrative examples are given.
Graef, John R., Webb, J. R. L.
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ELLIPTIC PROBLEMS WITH NONLOCAL CONDITIONS NEAR THE BOUNDARY
Mathematics of the USSR-Sbornik, 1987Let \(\Omega \subset R^ 2\) be a bounded domain with boundary \(\partial \Omega =(\cup^{N}_{i=1}\Gamma_ i)\cup K\) where \(\Gamma_ i\) is smooth, K is finite, and in a neigbourhood of points of K \(\partial \Omega\) is angular. Let \(\omega_{is}: \gamma_ i\to \Omega\) be nonsingular smooth maps where \(\gamma_ i\) is a neighbourhood of \(\Gamma_ i ...
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