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We prove the existence and uniqueness of weak solution of a Neumann boundary problem for an elliptic partial differential equation (PDE for short) with a singular divergence term which can only be understood in a weak sense. A probabilistic…

Probability · Mathematics 2018-04-24 Xue Yang , Jing Zhang

We show that a wide range of overdetermined boundary problems for semilinear equations with position-dependent nonlinearities admits nontrivial solutions. The result holds true both on the Euclidean space and on compact Riemannian…

Analysis of PDEs · Mathematics 2017-11-27 Miguel Dominguez-Vazquez , Alberto Enciso , Daniel Peralta-Salas

We study two types of asymptotic problems whose common feature - and difficulty- is to exhibit oscillating Dirichlet boundary conditions : the main contribution of this article is to show how to recover the Dirichlet boundary condition for…

Analysis of PDEs · Mathematics 2012-05-22 Guy Barles , Elisabeth Mironescu

In this paper, the asymptotic behavior of the solutions of a monotone problem posed in a locally periodic oscillating domain is studied. Nonlinear monotone boundary conditions are imposed on the oscillating part of the boundary whereas the…

Analysis of PDEs · Mathematics 2024-01-30 S. Aiyappan , G. Cardone , C. Perugia , R. Prakash

In this paper we focus the attention on free boundary problems ruled by partial differential equations with nonstandard growth, presenting in particular some recent results. The interest in these problems stems from the diverse applications…

Analysis of PDEs · Mathematics 2026-03-17 Fausto Ferrari , Monica Jacob , Claudia Lederman

In this paper, we investigate the following nonlinear Schr\"odinger equation with Neumann boundary conditions: \begin{equation*} \begin{cases} -\Delta u+ \lambda u= f(u) & {\rm in} \,~ \Omega,\\ \displaystyle\frac{\partial u}{\partial…

Analysis of PDEs · Mathematics 2025-03-21 Xiaojun Chang , Vicenţiu D. Rădulescu , Yuxuan Zhang

In this paper we study quasilinear elliptic systems driven by variable exponent double phase operators involving fully coupled right-hand sides and nonlinear boundary conditions. The aim of our work is to establish an enclosure and…

Analysis of PDEs · Mathematics 2022-08-03 Umberto Guarnotta , Roberto Livrea , Patrick Winkert

In the first part of this article we deal with the existence of at least three non-trivial weak solutions of a nonlocal problem with nonstandard growth involving a nonlocal Robin type boundary condition. The second part of the article is…

Analysis of PDEs · Mathematics 2020-03-31 Sabri Bahrouni , Ariel Salort

In this paper we consider the existence and multiplicity of weak solutions for the following class of fractional elliptic problem \begin{equation}\label{00} \left\{\begin{aligned} (-\Delta)^{\frac{1}{2}}u + u &= Q(x)f(u)\;\;\mbox{in}\;\;\R…

Analysis of PDEs · Mathematics 2019-10-08 Claudianor O. Alves , César E. Torres Ledesma

We study solutions to a one-phase singular perturbation problem that arises in combustion theory and that formally approximates the classical one-phase free boundary problem. We introduce a natural density condition on the transition layers…

Analysis of PDEs · Mathematics 2023-02-28 Nikola Kamburov

In this paper, we prove that there exists a unique weak solution to the mixed boundary value problem for a general class of semilinear second order elliptic partial differential equations with singular coefficients. Our approach is…

Probability · Mathematics 2011-12-15 Xue Yang , Tusheng Zhang

This note introduces a class of nonlinear Neumann problems on balls expanding with the radii tending towards infinity. Performing singular perturbation arguments, we establish the corresponding concentration phenomenon and refined…

Analysis of PDEs · Mathematics 2019-09-24 Chiun-Chang Lee

In this work we establish existence and multiplicity of solutions for elliptic problem with nonlinear boundary conditions under strong resonance conditions at infinity. The nonlinearity is resonance at infinity and the reso- nance phenomena…

Analysis of PDEs · Mathematics 2015-07-30 Alzaki Fadlallah , Edcarlos D. Da Silva

In this paper, we are concerned with the existence and concentration phenomena of solutions for the following singularly perturbed fractional Schr\"{o}dinger problem \begin{align*} \varepsilon^{2s}(-\Delta)^su+V(x)u=f(u) \ \ \ \mbox{in} \ \…

Analysis of PDEs · Mathematics 2017-02-09 Hua Jin , Wenbin Liu , Jianjun Zhang

We investigate existence and uniqueness of solutions to second-order elliptic boundary value problems containing a power nonlinearity applied to a fractional Laplacian. We detect the critical power separating the existence from the…

Analysis of PDEs · Mathematics 2020-05-20 Nicola Abatangelo , Matteo Cozzi

We consider the Dirichlet problem for quasilinear elliptic equations with Musielak-Orlicz (p,q)-growth and non-logarithmic conditions on the coefficients. A sufficient Wiener-type condition for the regularity of a boundary point is…

Analysis of PDEs · Mathematics 2021-09-20 Oleksandr V. Hadzhy , Mykhailo V. Voitovych

This paper is concerned with a Neumann type problem for singularly perturbed fractional nonlinear Schr\"odinger equations with subcritical exponent. For some smooth bounded domain $\Omega\subset \mathbf R^n$, our boundary condition is given…

Analysis of PDEs · Mathematics 2016-11-22 Guoyuan Chen

We study existence of solutions for a boundary degenerate (or singular) quasilinear equation in a smooth bounded domain under Dirichlet boundary conditions. We consider a weighted $p-${L}aplacian operator with a coefficient that is {locally…

Analysis of PDEs · Mathematics 2021-02-10 Oscar Agudelo , Pavel Drábek

In the present paper, we consider the parabolic and hyperbolic inequalities with a singular potentials and with a critical nonlinearities in the annulus domain. The problems are studied with Neumann-type and Dirichlet-type boundary…

Analysis of PDEs · Mathematics 2024-02-09 Meiirkhan B. Borikhanov , Berikbol T. Torebek

We show the existence of a weak solution of a semilinear elliptic Dirichlet problem on an arbitrary open set. We make no assumptions about the open set, very mild regularity assumptions on the semilinearity, plus a coerciveness assumption…

Analysis of PDEs · Mathematics 2016-07-19 Reinhard Stahn