相关论文: Configuration spaces and multiple positive solutio…
In this paper, we investigate the existence of positive weak solutions to a nonlocal singular elliptic problem under Dirichlet boundary condition. Problem is settled in fractional Musielak-Sobolev spaces with variable order. The main tool…
In this paper, we demonstrate the existence of positive solutions for certain weakly coupled elliptic systems of sublinear growth under homogeneous Dirichlet boundary conditions. Our findings generalize existing results related to sublinear…
The main purpose of this paper is to exhibit a simple variational setting for finding fully nontrivial solutions to the weakly coupled elliptic system (1.1). We show that such solutions correspond to critical points of a…
We consider a slightly subcritical elliptic system with Dirichlet boundary conditions and a non-power nonlinearity in a bounded smooth domain. For this problem, standard compact embeddings cannot be used to guarantee the existence of…
We analyze the existence and multiplicity of positive solutions to a nonlocal elliptic problem involving the spectral fractional Laplace operator endowed with homogeneous mixed Dirichlet-Neumann boundary conditions and weighted critical…
We show that the number of solutions of a double singularly perturbed Schroedinger Maxwell system on a smooth bounded domain A depends on the topological properties of the domain. In particular if A is non contractible we obtain cat(A) + 1…
In this paper, we analyze the existence of solution for a fractional elliptic system coupled by critical nonlinearities and endowed with mixed Dirichlet-Neumann boundary conditions. By means of variational methods and an…
We consider nonlinear elliptic systems satisfying componentwise coercivity condition. The nonlinear terms have controlled growths with respect to the solution and its gradient, while the behaviour in the independent variable is governed by…
In the present paper, we study the existence and uniqueness of solutions to some nonlocal singular elliptic problem under Dirichlet boundary condition. Problem is settled in Musielak-Sobolev spaces.
We consider singular solutions to quasilinear elliptic equations under zero Dirichlet boundary condition. Under suitable assumptions on the nonlinearity we deduce symmetry and monotonicity properties of positive solutions via an improved…
We investigate qualitative properties of positive singular solutions of some elliptic systems in bounded and unbounded domains. We deduce symmetry and monotonicity properties via the moving plane procedure. Moreover, in the unbounded case,…
In this paper we consider a competitive weakly coupled elliptic system in which each species is attracted to a small region and repelled from its complement. In this setting, we establish the existence of infinitely many solutions and of a…
We study the existence and asymptotic behavior of solutions having positive and sign-changing components to the singularly perturbed system of elliptic equations \begin{equation*} \begin{cases} -\varepsilon^2\Delta…
We consider a class of singularly perturbed elliptic problems with nonautonomous asymptotically linear nonlinearities. The dependence on the spatial coordinates comes from the presence of a potential and of a function representing a…
We consider a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions in a bounded domain $\Omega\subset\R^{n}$ whose boundary has an $(n-2)$-dimensional singularity. Assuming $1<p<\frac{n+2}{n-2}$, we prove that,…
We consider positive solutions to a singular semilinear elliptic equation in bounded smooth domains, with zero Dirichlet boundary conditions. We provide some weak and strong maximum principles for the H^1_0 part of the solution that allow…
We study qualitative properties of positive singular solutions to a two-coupled elliptic system with critical exponents. This system is related to coupled nonlinear Schrodinger equations with critical exponents for nonlinear optics and…
In this paper, we deal with an elliptic problem with the Dirichlet boundary condition. We operate in Sobolev spaces and the main analytic tool we use is the Lax-Milgram lemma. First, we present the variational approach of the problem which…
We establish the existence of solutions to a weakly-coupled competitive system of polyharmonic equations in R^N which are invariant under a group of conformal diffeomorphisms, and study the behavior of least energy solutions as the coupling…
We establish a positivity property for a class of semilinear elliptic problems involving indefinite sublinear nonlinearities. Namely, we show that any nontrivial nonnegative solution is positive for a class of problems the strong maximum…