相关论文: Robin double-phase problems with singular and supe…
In this paper, we study the existence, nonexistence and multiplicity of positive solutions to the problem given by \begin{equation*} \label{1} \left\{\begin{split} \mathcal{L}u\: &= \lambda u^{q} + u^{p}, \quad u>0 ~~ \text{in} ~\Omega,…
In this paper, we prove the existence of a unique positive entropy solution to a fractional Laplacian problem involving nonlinear singular terms and also a non-negative bounded Radon measure as a source term.
We use a variational approach to study existence and regularity of solutions for a Neumann $p$-Laplacian problem with a reaction term on metric spaces equipped with a doubling measure and supporting a Poincar\'e inequality. Trace theorems…
In this paper, we investigate a class of critical Ambrosetti-Prodi type problems involving the sub-Laplacian on a Carnot group. Specifically, we consider \[ \left\{ \begin{aligned} -\Delta_{\mathbb{G}} u &= \lambda u + u_{+}^{2_{Q}^{*}-1} +…
Let $\Omega:=\left( a,b\right) \subset\mathbb{R}$, $m\in L^{1}\left( \Omega\right) $ and $\lambda>0$ be a real parameter. Let $\mathcal{L}$ be the differential operator given by $\mathcal{L}u:=-\phi\left( u^{\prime}\right) ^{\prime}+r\left(…
In this paper, a class of linear parabolic singularly perturbed second order differential equations of reaction-diffusion type with initial and Robin boundary conditions is considered. The solution u of this equation is smooth, whereas the…
In this paper, we present a series of Liouville-type theorems for a class of nonhomogeneous quasilinear elliptic equations featuring reactions that depend on the solution and its gradient. Specifically, we investigate equations of the form…
We study the perturbation by a critical term and a $(p-1)$-superlinear subcritical nonlinearity of a quasilinear elliptic equation containing a singular potential. By means of variational arguments and a version of the…
We study for the first time a two-phase free boundary problem in which the solution satisfies a Robin boundary condition. We consider the case in which the solution is continuous across the free boundary and we prove an existence and a…
In this paper, we want to study the asymptotic behavior of the first $p$-Laplacian eigenvalue, with Robin boundary conditions, with negative boundary parameter. In particular, we prove that the limit of the eigenfunctions is a viscosity…
In this paper we deal with the multiplicity of positive solutions to the fractional Laplacian equation \begin{equation*} (-\Delta)^{\frac{\alpha}{2}} u=\lambda f(x)|u|^{q-2}u+|u|^{2^{*}_{\alpha}-2}u, \quad\text{in}\,\,\Omega,…
We consider a Dirichlet problem driven by the anisotropic $(p,q)$-Laplacian and a reaction with gradient dependence (convection). The presence of the gradient in the source term excludes from consideration a variational approach in dealing…
We analyze bound states of Robin Laplacian in infinite planar domains with a smooth boundary, in particular, their relations to the geometry of the latter. The domains considered have locally straight boundary being, for instance, locally…
In this paper, we consider the large-time behavior of solutions of a reaction diffusion system arising from a nuclear reactor model with the Robin boundary conditions, which consists of two real-valued unknown functions. In particular, we…
In this paper we consider the recurrent equation $$\Lambda_{p+1}=\frac1p\sum_{q=1}^pf\bigg(\frac{q}{p+1}\bigg)\Lambda_{q}\Lambda_{p+1-q}$$ for $p\ge 1$ with $f\in C[0,1]$ and $\Lambda_1=y>0$ given. We give conditions on $f$ that guarantee…
We study the asymptotic behaviour, as $p\to 1^{+}$, of the solutions of the following inhomogeneous Robin boundary value problem: \begin{equation} \label{pbabstract} \tag{P} \left\{\begin{array}{ll} \displaystyle -\Delta_p u_p = f &…
In this paper, we show existence of \textit{continuums} of positive solutions for non-local quasilinear problems with strongly-singular reaction term on a bounded domain in $\mathbb{R}^N$ with $N \geq 2$. We approached non-autonomous and…
In this article we establish an approximation result involving the Laplacian with Robin boundary conditions. It informs about the weak solutions dependence from the input function on the boundary.
We study the global structure of the set of radial solutions of a nonlinear Dirichlet problem involving the p-Laplacian with p>2, in the unit ball of $R^N$, $N \ges 1$. We show that all non-trivial radial solutions lie on smooth curves of…
We write down a Robin boundary term for general relativity. The construction relies on the Neumann result of arXiv:1605.01603 in an essential way. This is unlike in mechanics and (polynomial) field theory, where two formulations of the…