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An initial-boundary value problem with homogeneous Dirichlet boundary conditions for three-dimensional Zakharov-Kuznetsov equation is considered. Results on global existence, uniqueness and large-time decay of weak solutions in certain…

Analysis of PDEs · Mathematics 2015-06-26 Andrei V. Faminskii

We consider a nonlinear eigenvalue problem under Robin boundary conditions in a domain with (possibly noncompact) smooth boundary. The problem involves a weighted p-Laplacian operator and subcritical nonlinearities satisfying…

Analysis of PDEs · Mathematics 2013-05-10 Kanishka Perera , Patrizia Pucci , Csaba Varga

We consider a number of boundary value problems involving the $p$-Laplacian. The model case is $-\Delta_p u=V|u|^{p-2}u$ for $u\in W_0^{1,2}(D)$ with $D$ a bounded domain in ${\bf R}^n$. We derive necessary conditions for the existence of…

Analysis of PDEs · Mathematics 2013-02-19 Julian Edward , Steve Hudson , Mark Leckband

We prove the existence and uniqueness of solutions to a Dirichlet problem \[ \begin{cases} Lu = f + v^{-1}\text{Div}(v{\bf e} h), & x \in \Omega; u = 0, & x \in \partial \Omega, \end{cases}\] where $L$ is a degenerate, linear, second order…

Analysis of PDEs · Mathematics 2025-07-08 Seyma Cetin , David Cruz-Uribe , Feyza Elif Dal , Scott Rodney , Yusuf Zeren

We consider a nonlinear Dirichlet problem driven by the $p$-Laplace differential operator with a reaction which has a subcritical growth restriction only from above. We prove two multiplicity theorems producing three nontrivial solutions,…

Analysis of PDEs · Mathematics 2019-03-13 Nikolaos S. Papageorgiou , Vicenţiu D. Rădulescu , Dušan D. Repovš

Two-point boundary value problems for a discrete Ermakov-Painlev\'e II equation are analysed by means of topological methods. In addition, an alternative variational approach is detailed. Existence of solutions is established for…

Classical Analysis and ODEs · Mathematics 2025-08-13 Pablo Amster , Colin Rogers

We consider the boundary value problem associated to the divergence operator with vanishing Dirichlet boundary conditions and we prove the existence of classical solutions under slight assumptions on the regularity of the datum.

Analysis of PDEs · Mathematics 2017-12-22 Luigi C. Berselli , Placido Longo

We establish existence and multiplicity theorems for a Dirichlet boundary value problem at resonance, which is a nonlinear subcritical perturbation of a linear eigenvalue problem studied by Cuesta. Our framework includes a sign-changing…

Analysis of PDEs · Mathematics 2007-05-23 Teodora Liliana Dinu

This paper is devoted to establishing results for semilinear elliptic boundary value problems where the solvability of problems subject to {\it No Flux} boundary conditions follows from the solvability of related {\it Dirichlet} boundary…

Analysis of PDEs · Mathematics 2012-07-03 Loc Hoang Nguyen , Klaus Schmitt

This paper studies a nonlinear Dirichlet problem for the $p$-Laplacian operator with nonlinearity consisting of power components. The problem under consideration can be though of as a perturbation of the Ambrosetti-Brezis-Cerami problem…

Analysis of PDEs · Mathematics 2015-01-19 Vladimir Lubyshev

We show the existence and uniqueness as well as boundedness of weak solutions to linear elliptic equations with $L^2$-drifts of negative divergence and singular zero-order terms which are positive. Our main target is to show the…

Analysis of PDEs · Mathematics 2023-09-26 Haesung Lee

In this work, we study the existence and multiplicity of solutions for the following problem \begin{equation}\label{probaa1} \left\{ \begin{aligned} -(\Delta)_{p}^{s} u + V(x)|u|^{p-2}u &= \lambda f(u),&x\in\Omega; u&=0,&x\in…

Analysis of PDEs · Mathematics 2025-05-20 Emer Lopera , Leandro Recôva , Adolfo Rumbos

We consider inverse boundary value problems for elliptic equations of second order of determining coefficients by Dirichlet-to-Neumann map on subboundaries, that is, the mapping from Dirichlet data supported on $\partial\Omega\setminus…

Mathematical Physics · Physics 2013-03-12 Oleg Yu Imanuvilov , M. Yamamoto

We focus on the study of $p$-Laplacian Dirichlet problem containing the left and right fractional derivative operators. By using the genus properties in critical point theory, we establish some new criteria to guarantee the existence of…

Classical Analysis and ODEs · Mathematics 2016-06-27 Taiyong Chen , Wenbin Liu , Hua Jin

We study a class of fractional $p$-Laplacian problems with weights which are possibly singular on the boundary of the domain. We provide existence and multiplicity results as well as characterizations of critical groups and related…

Analysis of PDEs · Mathematics 2016-03-21 Ky Ho , Kanishka Perera , Inbo Sim , Marco Squassina

We study a Dirichlet boundary value problem associated to an anisotropic differential operator on a smooth bounded of $\Bbb R^N$. Our main result establishes the existence of at least two different non-negative solutions, provided a certain…

Analysis of PDEs · Mathematics 2009-11-11 Mihai Mihailescu , Vicentiu Radulescu

In this article, we prove the existence of at least three positive solutions for the following nonlocal singular problem \begin{equation*} (P_\la)\left\{ \begin{split} (-\De)^su &= \la\frac{f(u)}{u^q}, \; \; u>0 \;\; \text{in}\;\; \Om,\\ u…

Analysis of PDEs · Mathematics 2018-01-22 Jacques Giacomoni , Tuhina Mukherjee , Konijeti Sreenadh

We study an inverse boundary value problem associated with $p$-Laplacian which is further perturbed by a linear second order term, defined on a bounded set $\Omega$ in $\R^n, n\geq 2$. We recover the coefficients at the boundary from the…

Analysis of PDEs · Mathematics 2024-01-12 Nitesh Kumar , Tanmay Sarkar , Manmohan Vashisth

We study the existence of positive solutions for a class of double phase Dirichlet equations which have the combined effects of a singular term and of a parametric superlinear term. The differential operator of the equation is the sum of a…

Analysis of PDEs · Mathematics 2021-05-17 Nikolaos S. Papageorgiou , Dušan D. Repovš , Calogero Vetro

In this paper we give a comprehensive treatment of a two-penalty boundary obstacle problem for a divergence form elliptic operator, motivated by applications to fluid dynamics and thermics. Specifically, we prove existence, uniqueness and…

Analysis of PDEs · Mathematics 2020-05-13 Donatella Danielli , Brian Krummel