Related papers: Robin problems with indefinite linear part and com…
In this paper we study the $p$-Poisson equation with Robin boundary conditions, where the Robin parameter is a function. By means of some weighted isoperimetric inequalities, we provide various sharp bounds for the solutions to the problems…
We analyze, mainly using bifurcation methods, an elliptic superlinear problem in one-dimension with periodic boundary conditions. One of the main novelties is that we follow for the first time a bifurcation approach, relying on a…
In this paper, we consider the principal eigenvalue problem for Hormander's laplacian on $R^n$. We also study a related semi-linear sub-elliptic equation in the whole $R^n$ and prove that under a suitable condition, we have infinite many…
The main goal of this paper is to address an important conjecture in the field of differential equations in the presence of a harmonic potential. While in the subcritical case, the uniqueness of positive solution has been addressed by…
By using a suitable topological argument based on cohomological linking and by exploiting a Trudinger-Moser inequality in fractional spaces recently obtained, we prove existence of multiple solutions for a problem involving the nonlinear…
We establish the existence and multiplicity of positive solutions to the problems involving the fractional Laplacian: \begin{equation*} \left\{\begin{array}{lll} &(-\Delta)^{s}u=\lambda u^{p}+f(u),\,\,u>0 \quad &\mbox{in}\,\,\Omega,\\…
We consider a slightly subcritical Dirichlet problem with a non-power nonlinearity in a bounded smooth domain. For this problem, standard compact embeddings cannot be used to guarantee the existence of solutions as in the case of power-type…
Let $\Omega=(a,b)\subset\mathbb{R}$, $0\leq m,n\in L^{1}(\Omega)$, $\lambda,\mu>0$ be real parameters, and $\phi:\mathbb{R}\rightarrow\mathbb{R}$ be an odd increasing homeomorphism. In this paper we consider the existence of positive…
We show that the spectrum of a Schr\"odinger eigenvalue problem posed on a closed Riemannian manifold $M$ with non-negative potential can be approached by that of Robin eigenvalue problems with constant positive boundary parameter posed on…
In this paper we prove the existence of at least one positive solution for the nonlocal semipositone problem \[ \displaystyle \left\{\begin{array}{rcll} (-\Delta)_p^s(u) &=& \lambda f(u) \qquad & \text{in} \ \ \Omega \\u &=& 0 & \text{in} \…
This paper is concerned with a quaslinear parabolic equation including a nonlinear nonlocal initial condition. The problem arises as equilibrium equation in population dynamics with nonlinear diffusion. We make use of global bifurcation…
Boundary value problems for second-order elliptic equations in divergence form, whose nonlinearity is governed by a convex function of non-necessarily power type, are considered. The global boundedness of their solutions is established…
In this paper, we deal with the existence and multiplicity of solutions to the nonuniformly elliptic equation of the N-Lapalcian type with a potential and a nonlinear term of critical exponential growth and satisfying the…
In this work, we consider static manifolds $M$ with nonempty boundary $\partial M$. In this case, we suppose that the potential $V$ also satisfies an overdetermined Robin type condition on $\partial M$. We prove a rigidity theorem for the…
We proceed with the investigation of the problem $(P_\lambda): $ $-\Delta u = \lambda b(x)|u|^{q-2}u +a(x)|u|^{p-2}u \ \mbox{ in } \Omega, \ \ \frac{\partial u}{\partial \mathbf{n}} = 0 \ \mbox{ on } \partial \Omega$, where $\Omega$ is a…
We study the semiflow $\mathcal{S}(t)$ defined by a semilinear parabolic equation with a singular square potential $V(x)=\frac{\mu}{|x|^2}$. It is known that the Hardy-Poincar\'{e} inequality and its improved versions, have a prominent role…
We study the asymptotic behavior as $p\to\infty$ of the Gelfand problem \[ -\Delta_{p} u=\lambda\,e^{u}\ \textrm{in}\ \Omega\subset\mathbb{R}^n,\quad u=0 \ \textrm{on}\ \partial\Omega. \] Under an appropriate rescaling on $u$ and $\lambda$,…
We study a nonlinear parametric Neumann problem driven by a nonhomogeneous quasilinear elliptic differential operator $\operatorname{div}(a(x,\nabla u))$, a special case of which is the $p$-Laplacian. The reaction term is a nonlinearity…
Hybrid inverse problems are mathematical descriptions of coupled-physics (also called multi-waves) imaging modalities that aim to combine high resolution with high contrast. The solution of a high-resolution inverse problem, a first step…
By means of a suitable weighted rearrangement, we obtain various apriori bounds for the solutions to a Robin problem. Among other things, we derive a family of Faber-Krahn type inequalities.