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We show that the spectrum of a Schr\"odinger eigenvalue problem posed on a closed Riemannian manifold $M$ with non-negative potential can be approached by that of Robin eigenvalue problems with constant positive boundary parameter posed on…

Spectral Theory · Mathematics 2024-11-05 Chia-Chun Lo

By applying Ricceri's variational principle, we demonstrate the existence of solutions for the following Robin problem \begin{equation*}\left\{ \begin{array}{cc}-\func{div}\left( \omega _{1}(x)\left\vert \nabla u\right\vert^{p(x)-2}\nabla…

Analysis of PDEs · Mathematics 2020-12-15 Ismail Aydin , Cihan Unal

We consider a fractional double phase Robin problem involving variable order and variable exponents. The nonlinearity $f$ is a Carath\'{e}odory function satisfying some hypotheses which do not include the Ambrosetti-Rabinowitz type…

Analysis of PDEs · Mathematics 2022-05-04 Reshmi Biswas , Sabri Bahrouni , Marcos L. Carvalho

In this paper, I derive the limiting behaviour of the solutions to Poisson's equation, in a perforated domain, subject to inhomogeneous Robin boundary conditions. In the first half of the paper, I derive a generalised limit for non-periodic…

Analysis of PDEs · Mathematics 2022-10-04 Aaron Pim

In this work, we study the unique continuation properties of Robin boundary value problems with Robin potentials $\eta \in L_{d-1+\varepsilon}$. Our results generalize earlier ones in which $\eta$ was assumed to be either zero (Neumann…

Analysis of PDEs · Mathematics 2025-01-17 Zongyuan Li

In this paper we use variational methods to establish the existence of solutions for a class of nonlinear elliptic problems involving a combined convolution-type and Hardy nonlinearity with subcritical and critical growth.

Analysis of PDEs · Mathematics 2026-04-09 Guangze Gu , Aleks Jevnikar

We deal with the existence of weak solutions for a mixed Neumann-Robin-Cauchy problem. The existence results are based on global-in-time estimates of approximating solutions, and the passage to the limit exploits compactness techniques. We…

Analysis of PDEs · Mathematics 2017-01-11 Luisa Consiglieri

The classical local Neumann problem is well studied and solutions of this problem lie, in general, in a Sobolev space. In this work, we focus on nonlocal Neumann problems with measurable, nonnegative kernels, whose solutions require less…

Analysis of PDEs · Mathematics 2022-08-11 Leonhard Frerick , Christian Vollmann , Michael Vu

This paper is concerned with a biharmonic equation under the Navier boundary condition with nearly critical exponent. We study the asymptotic behavior os solutions which are minimizing for the Sobolev quatient. We show that such solutions…

Analysis of PDEs · Mathematics 2007-05-23 Mohamed Ben Ayed , Khalil El Mehdi

The paper is concerned with the existence and multiplicity of positive solutions of the nonhomogeneous Choquard equation over an annular type bounded domain. Precisely, we consider the following equation \[ -\De u =…

Analysis of PDEs · Mathematics 2019-03-11 Divya Goel , K. Sreenadh

We compare the solutions of two Poisson problems in a spherical shell with Robin boundary conditions, one with given data, and one where the data has been cap symmetrized. When the Robin parameters are nonnegative, we show that the solution…

Analysis of PDEs · Mathematics 2021-01-08 Jeffrey J. Langford

This article deals with a survey of recent developments and results on Choquard equations where we focus on the existence and multiplicity of solutions of the partial differential equations which involve the nonlinearity of convolution…

Analysis of PDEs · Mathematics 2018-11-13 Tuhina Mukherjee , K. Sreenadh

In this paper, we prove a threshold result for the Robin problem of semilinear parabolic equations

Analysis of PDEs · Mathematics 2010-03-22 Junhui Xie , Qiuyi Dai , Huaxiang Hu

We study a nonlinear boundary value problem driven by the $p$-Laplacian plus an indefinite potential with Robin boundary condition. The reaction term is a Carath\'eodory function which is asymptotically resonant at $\pm\infty$ with respect…

Analysis of PDEs · Mathematics 2017-07-04 Nikolaos S. Papageorgiou , Vicenţiu D. Rădulescu , Dušan D. Repovš

The paper is devoted to the penalty Robin-Robin domain decomposition methods (DDMs), proposed by us for the solution of unilateral multibody contact problems of elasticity. These DDMs are based on the penalty method for variational…

Numerical Analysis · Mathematics 2015-04-28 Ivan I. Dyyak , Ihor I. Prokopyshyn , Ivan A. Prokopyshyn

In this article a special class of nonlinear optimal control problems involving a bilinear term in the boundary condition is studied. These kind of problems arise for instance in the identification of an unknown space-dependent Robin…

Numerical Analysis · Mathematics 2024-12-20 Max Winkler

We consider a system of particles undergoing correlated diffusion with elastic boundary conditions on the half-line. By taking the large particle limit we establish existence and uniqueness for the limiting empirical measure valued process…

Probability · Mathematics 2022-10-19 Ben Hambly , Julian Meier , Andreas Sojmark

In the current work we study a nonlocal parabolic problem with Robin boundary conditions. The problem arises from the study of an idealized electrically actuated MEMS (Micro-Electro-Mechanical System) device. Initially we study the…

Analysis of PDEs · Mathematics 2021-04-13 Ourania Drosinou , Nikos I. Kavallaris , Christos V. Nikolopoulos

The paper is devoted to the study of positive solutions of a second-order linear elliptic equation in divergence form in a domain $D\subseteq \mathbb{R}^n$ that satisfy an oblique boundary condition on a portion of $\partial D$. First, we…

Analysis of PDEs · Mathematics 2020-08-11 Yehuda Pinchover , Idan Versano

The phase transitions and critical properties of two types of inhomogeneous systems are reviewed. In one case, the local critical behaviour results from the particular shape of the system. Here scale-invariant forms like wedges or cones are…

Statistical Mechanics · Physics 2009-10-22 F. Iglói , I. Peschel , L. Turban