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In this paper, we study a broad class of fully nonlinear elliptic equations on Hermitian manifolds. On one hand, under the optimal structural assumptions we derive $C^{2,\alpha}$-estimate for solutions of the equations on closed Hermitian…

Analysis of PDEs · Mathematics 2025-03-17 Rirong Yuan

We consider semilinear elliptic equations with double power nonlineaities. The condition to assure the existence of positive solutions is well-known. In the present paper, we remark that the additional condition to assure uniqueness…

Analysis of PDEs · Mathematics 2008-11-07 Shinji Kawano

This paper deals with existence and multiplicity of positive solutions for a quasilinear problem with Neumann boundary conditions, set in a ball. The problem admits at least one constant non-zero solution and it involves a nonlinearity that…

Analysis of PDEs · Mathematics 2020-02-28 Francesca Colasuonno , Benedetta Noris

Under structural conditions which are almost optimal, we derive a quantitative version of boundary estimate then prove existence of solutions to Dirichlet problem for a class of fully nonlinear elliptic equations on Hermitian manifolds.

Analysis of PDEs · Mathematics 2021-06-29 Rirong Yuan

In this paper, we deal with a class of semilinear elliptic equation in a bounded domain $\Omega\subset\mathbb{R}^N$, $N\geq 3$, with $C\sp{1,1}$ boundary. Using a new fixed point result of the Krasnoselskii's type for the sum of two…

Analysis of PDEs · Mathematics 2007-05-23 Cleon S. Barroso

We consider a parametric semilinear Robin problem driven by the Laplacian plus an indefinite potential. The reaction term involves competing nonlinearities. More precisely, it is the sum of a parametric sublinear (concave) term and a…

Analysis of PDEs · Mathematics 2019-09-11 N. S. Papageorgiou , V. D. Rădulescu , D. D. Repovš

We consider a nonlinear Dirichlet problem driven by a nonhomogeneous differential operator with a growth of order $(p-1)$ near $+\infty$ and with a reaction which has the competing effects of a parametric singular term and a…

Analysis of PDEs · Mathematics 2020-04-28 Nikolaos S. Papageorgiou , Vicenţiu D. Rădulescu , Dušan D. Repovš

This study is devoted to proving the existence of weak solutions for a nonlinear elliptic problem with Neumann-type boundary data. The problem is driven by a discontinuous power nonlinearity and a nonsmooth prescribed data. Additionally, we…

Analysis of PDEs · Mathematics 2026-04-28 Debajyoti Choudhuri , Dušan D. Repovš , Kamel Saoudi

We establish a priori $L^\infty$-estimates for non-negative solutions of a semilinear nonlocal Neumann problem. As a consequence of these estimates, we get non-existence of non-constant solutions under suitable assumptions on the diffusion…

Analysis of PDEs · Mathematics 2023-09-27 Eleonora Cinti , Francesca Colasuonno

It is established existence, multiplicity and asymptotic behavior of positive solutions for a quasilinear elliptic problem driven by the $\Phi$-Laplacian operator. One of these solutions is obtained as ground state solution by applying the…

Analysis of PDEs · Mathematics 2016-10-18 C. Goulart , E. D. da Silva , M. L. M. Carvalho , J. V. Goncalves

In this paper we study the multiplicity of positive solutions for nonlinear elliptic equations on $\R^N$. The number of solutions is greater or equal than the number of disjoint intervals on which the nonlinear term is negative.…

Analysis of PDEs · Mathematics 2013-04-12 Claudio Bonanno

In this paper we prove that positive weak solutions for quasilinear parabolic equations on bounded domains subject to homogenous Neumann boundary conditions becme classical and global under the unique condition that the reaction doesn't…

Dynamical Systems · Mathematics 2024-09-11 Said Kouachi

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

This paper deals with a class of singularly perturbed nonlinear elliptic problems $(P_\e)$ with subcritical nonlinearity. The coefficient of the linear part is assumed to concentrate in a point of the domain, as $\e\to 0$, and the domain is…

Analysis of PDEs · Mathematics 2013-10-29 Riccardo Molle

In this paper we obtain existence results for the positive solution of a singular elliptic boundary value problem. To prove the main results we use comparison arguments and the method of sub-super solutions combined with a procedure which…

Analysis of PDEs · Mathematics 2011-05-16 Dragos-Patru Covei

Our purpose is to find positive solutions $u \in D^{1,2}(\rz^N)$ of the semilinear elliptic problem $-\laplace u - \lambda V(x) u = h(x) u^{p-1}$ for $2<p$. The functions $V$ and $h$ may have an indefinite sign and the linearized operator…

Analysis of PDEs · Mathematics 2007-05-23 Matthias Schneider

The main thrust of our current work is to exploit very specific characteristics of a given problem in order to acquire improved compactness for supercritical problems and to prove existence of new types of solutions. To this end, we shall…

Analysis of PDEs · Mathematics 2022-06-28 Craig Cowan , Abbas Moameni

In this work we analyze the existence of solutions to the nonlinear elliptic system: \begin{equation*} \left\{ \begin{array}{rcll} -\Delta u & = & v^q+\a g & \text{in }\Omega , \\ -\Delta v& = &|\nabla u|^{p}+\l f &\text{in }\Omega , \\…

Analysis of PDEs · Mathematics 2017-09-12 Boumediene Abdellaoui , Ahmed Attar , El-Haj Laamri

In a previous paper we considered a class of infinitely degenerate quasilinear equations and derived a priori bounds for high order derivatives of solutions in terms of the Lipschitz norm. We now show that it is possible to obtain bounds…

Analysis of PDEs · Mathematics 2011-03-17 Cristian Rios , Eric Sawyer , Richard Wheeden

We establish the existence of weak solutions of a nonlinear radiation-type boundary value problem for elliptic equation on divergence form with discontinuous leading coefficient. Quantitative estimates play a crucial role on the real…

Analysis of PDEs · Mathematics 2015-07-23 Luisa Consiglieri