Related papers: Positive solutions for nonlinear nonhomogeneous pa…

In this paper, we prove a threshold result for the Robin problem of semilinear parabolic equations

We study second order parabolic equations on Lipschitz domains subject to inhomogeneous Neumann (or, more generally, Robin) boundary conditions. We prove existence and uniqueness of weak solutions and their continuity up to the boundary of…

In this paper we consider an anisotropic Robin problem driven by the $p(x)$-Laplacian and a superlinear reaction. Applying variational tools along with truncation and comparison techniques as well as critical groups, we prove that the…

We study a nonlinear boundary value problem driven by the $p$-Laplacian plus an indefinite potential with Robin boundary condition. The reaction term is a Carath\'eodory function which is asymptotically resonant at $\pm\infty$ with respect…

We study a superlinear and subcritical Kirchhoff type equation which is variational and depends upon a real parameter $\lambda$. The nonlocal term forces some of the fiber maps associated with the energy functional to have two critical…

We study a Dirichlet problem driven by the degenerate fractional p-Laplacian and involving a nonlinear reaction, which depends on a positive parameter. The reaction is assumed to be (p-1)-sublinear near the origin and (p-1)-superlinear at…

In the work we consider a boundary value problem for a second order equation with variable coefficients in a multi-dimensional domain perforated by small cavities closely spaced along a given manifold. We assume that the linear sizes of all…

We consider perturbations of nonlinear eigenvalue problems driven by a nonhomogeneous differential operator plus an indefinite potential. We consider both sublinear and superlinear perturbations and we determine how the set of positive…

In \cite{CJ1} M. Jaoua et al. studied the linear approximation of Robin problem on $\Omega$ an open bounded domain of $\R^d$, and they given some important results. In this paper, we study a nonlinear approximation of an elliptic problem…

Let $\Omega\subset\mathbb{R}^{N}$ ($N\geq1$) be a smooth bounded domain, $a\in C(\bar{\Omega})$ a sign-changing function, and $0\leq q<1$. We investigate the Robin problem \[ \begin{cases} -\Delta u=a(x)u^{q} & \mbox{in $\Omega$},\\ u\geq0…

The paper studies families of positive solution curves for non-autonomous two-point problems \[ u"+\lambda f(u)-\mu g(x)=0, \;\; -1<x<1, \;\; u(-1)=u(1)=0 \] depending on two positive parameters $\lambda$ and $\mu$. We regard $\lambda$ as a…

In the present paper we deal with a quasilinear problem involving a singular term and a parametric superlinear perturbation. We are interested in the existence, nonexistence and multiplicity of positive solutions as the parameter…

We study an inverse boundary value problem in corrosion detection. The model is based on a conductivity equation with nonlinear Robin boundary condition. We prove that the nonlinear Robin term can be identified locally from Cauchy data…

In this paper we consider the existence of positive solutions for a singular elliptic problem involving an asymtotically linear nonlinearity and depending on one positive parameter. Using variational methods, together with comparison…

We study the second-order boundary value problem \begin{equation*} \begin{cases} \, -u''=a_{\lambda,\mu}(t) \, u^{2}(1-u), & t\in(0,1), \\ \, u'(0)=0, \quad u'(1)=0, \end{cases} \end{equation*} where $a_{\lambda,\mu}$ is a step-wise…

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(…

We consider the nonlinear Schr\"{o}dinger equation on the half-line $x \geq 0$ with a Robin boundary condition at $x = 0$ and with initial data in the weighted Sobolev space $H^{1,1}(\mathbb{R}_+)$. We prove that there exists a global weak…

The paper studies the large-time behavior of solutions to the Robin problem for PDEs with critical nonlinearities. For the considered problems, nonexistence results are obtained, which complements the interesting recent results by Ikeda et…

It is shown that globally positive solutions of a linear second order parabolic partial differential equation on a bounded domain, with Robin boundary conditions, are unique up to multiplication by a positive constant.

This paper is devoted to the existence of positive solutions for a problem related to a fourth-order differential equation involving a nonlinear term depending on a second order differential operator, $$(-\Delta)^2 u=\lambda u+…