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We study the multiplicity of positive solutions for a two-point boundary value problem associated to the nonlinear second order equation $u''+f(x,u)=0$. We allow $x \mapsto f(x,s)$ to change its sign in order to cover the case of scalar…

Classical Analysis and ODEs · Mathematics 2015-12-17 Guglielmo Feltrin , Fabio Zanolin

We consider the semilinear elliptic problem \begin{equation}\label{problemAbstract} \left\{\begin{array}{lr}-\Delta u= |u|^{p-1}u\qquad \mbox{ in }B\\ u=0\qquad\qquad\qquad\mbox{ on }\partial B \end{array}\right.\tag{$\mathcal E_p$}…

Analysis of PDEs · Mathematics 2017-09-12 Francesca Gladiali , Isabella Ianni

In this paper, we study the existence and multiplicity results of nontrivial positive solutions to a quasilinear elliptic equation in $\RN$, when $N\geq2$, as \begin{equation} \Lp…

Analysis of PDEs · Mathematics 2020-03-18 Qi Han

We establish some existence and regularity results to the Dirichlet problem, for a class of quasilinear elliptic equations involving a partial differential operator, depending on the gradient of the solution. Our results are formulated in…

Analysis of PDEs · Mathematics 2022-07-22 Giuseppina Barletta , Elisabetta Tornatore

We prove an existence theorem for positive solutions to Lichnerowicz-type equations on complete manifolds with boundary and nonlinear Neumann conditions. This kind of nonlinear problems arise quite naturally in the study of solutions for…

Analysis of PDEs · Mathematics 2017-08-16 Guglielmo Albanese , Marco Rigoli

We show the existence of solution for some classes of nonlocal problems. Our proof combines the presence of sub and supersolution with the pseudomonotone operators theory.

Analysis of PDEs · Mathematics 2014-02-11 Claudianor O. Alves , Dragos-Patru Covei

We show the existence of nontrivial stationary weak solutions to the surface quasi-geostrophic equations on the two dimensional periodic torus.

Analysis of PDEs · Mathematics 2021-12-01 Xinyu Cheng , Hyunju Kwon , Dong Li

In the framework of the nonsmooth critical point theory for lower semi-continuous functionals, we propose a direct variational approach to investigate the existence of infinitely many weak solutions for a class of semi-linear elliptic…

Analysis of PDEs · Mathematics 2013-05-14 Pietro d'Avenia , Eugenio Montefusco , Marco Squassina

In this paper, we study the existence of solutions for second-order non-instantaneous impulsive differential equations with a perturbation term. By variational approach, we obtain the problem has at least one solution under assumptions that…

Analysis of PDEs · Mathematics 2021-03-31 Wangjin Yao , Liping Dong , Jing Zeng

We consider a non-polynomial cubic spline to develop the classes of methods for the numerical solution of singularly perturbed two-point boundary value problems. The proposed methods are second and fourth order accurate and applicable to…

Numerical Analysis · Mathematics 2012-06-13 Islam Khan , Tariq Aziz

In this paper we prove an existence result to the problem $$\left\{\begin{array}{ll} -\Delta u = |u|^{p-1} u \qquad & \text{in} \Omega, \\ u= 0 & \text{on} \partial\Omega, \end{array} \right. $$ where $\Omega$ is a bounded domain in…

Analysis of PDEs · Mathematics 2020-01-27 Anna Lisa Amadori , Francesca Gladiali , Massimo Grossi

We study the existence of sign-changing solutions with multiple bubbles to the slightly subcritical problem $$-\Delta u=|u|^{2^*-2-\e}u \hbox{in}\Omega, \quad u=0 \hbox{on}\partial \Omega,$$ where $\Omega$ is a smooth bounded domain in…

Analysis of PDEs · Mathematics 2015-10-28 Thomas Bartsch , Teresa D'Aprile , Angela Pistoia

We investigate partial symmetry of solutions to semi-linear and quasi-linear elliptic problems with convex nonlinearities, in domains that are either axially symmetric or radially symmetric.

Analysis of PDEs · Mathematics 2012-08-13 Kanishka Perera , Marco Squassina

In this paper, we mainly establish the existence of at least three non-trivial solutions for a class of nonhomogeneous quasilinear elliptic systems with Dirichlet boundary value or Neumann boundary value in a bounded domain…

Analysis of PDEs · Mathematics 2024-06-28 Xiaoli Yu , Xingyong Zhang

The aim of this work is to establish the existence of multi-peak solutions for the following class of quasilinear problems \[ - \mbox{div}\big(\epsilon^{2}\phi(\epsilon|\nabla u|)\nabla u\big) + V(x)\phi(| u|)u = f(u)\quad \mbox{in} \quad…

Analysis of PDEs · Mathematics 2016-08-15 Claudianor O. Alves , Ailton R. da Silva

We prove the existence of weak solutions for the one obstacle problem associated with a class of quasilinear wave equations in one space dimension, extending previous results obtained in the linear case, and we also address the two…

Analysis of PDEs · Mathematics 2026-04-02 João Paulo Dias , Wladimir Neves , José Francisco Rodrigues

We study a nonlinear, nonhomogeneous elliptic equation with an asymmetric reaction term depending on a positive parameter, coupled with Robin boundary conditions. Under appropriate hypotheses on both the leading differential operator and…

Analysis of PDEs · Mathematics 2017-10-20 Antonio Iannizzotto , Monica Marras , Nikolaos S. Papageorgiou

We introduce a method for solving Calder\'on type inverse problems for semilinear equations with power type nonlinearities. The method is based on higher order linearizations, and it allows one to solve inverse problems for certain…

Analysis of PDEs · Mathematics 2019-04-01 Matti Lassas , Tony Liimatainen , Yi-Hsuan Lin , Mikko Salo

We provide new results on the existence, non-existence and multiplicity of non-negative radial solutions for semilinear elliptic systems with Neumann boundary conditions on an annulus. Our approach is topological and relies on the classical…

Analysis of PDEs · Mathematics 2019-02-12 Filomena Cianciaruso , Gennaro Infante , Paolamaria Pietramala

This paper deals with solutions to the equation \begin{equation*} -\Delta u = \lambda_+ \left(u^+\right)^{q-1} - \lambda_- \left(u^-\right)^{q-1} \quad \text{in $B_1$} \end{equation*} where $\lambda_+,\lambda_- > 0$, $q \in (0,1)$,…

Analysis of PDEs · Mathematics 2018-03-20 Nicola Soave , Susanna Terracini