Related papers: Multiple solutions for a nonlinear and non-homogen…
In this paper, we study the existence and multiplicity of solutions for the following fractional problem involving the Hardy potential and concave-convex nonlinearities: $$({-}{ \Delta})^{\frac{\alpha}{2}}u- \gamma \frac{u}{|x|^{\alpha}}=…
We study the multiplicity of positive solutions for a two-point boundary value problem associated to the nonlinear second order equation $u''+f(x,u)=0$. We allow $x \mapsto f(x,s)$ to change its sign in order to cover the case of scalar…
In this paper, we study the Sobolev regularity of solutions to nonlinear second order elliptic equations with super-linear first-order terms on Riemannian manifolds, complemented with Neumann boundary conditions, when the source term of the…
In this paper, we consider nonlinearly perturbed Legendre differential equations subject to the usual boundary conditions. For such problems we establish sufficient conditions for the existence of solutions and in some cases we provide a…
In the paper we consider a boundary value problem involving a differential equation with the fractional Laplacian $(-\Delta)^{\alpha/2}$ for $\alpha \in\left( 1,2\right) $ and some superlinear and subcritical nonlinearity $G_{z}$ provided…
We analyze strict positivity at the boundary for nonnegative solutions of Robin problems in general (non-smooth) domains, e.g. open sets with rectifiable topological boundaries having finite Hausdorff measure. This question was raised by…
Multiple solutions are common in various non-convex problems arising from industrial and scientific computing. Nonetheless, understanding the nontrivial solutions' qualitative properties seems limited, partially due to the lack of efficient…
The evolution of two isothermal, incompressible, immiscible fluids in a bounded domain is governed by Cahn-Hilliard-Navier-Stokes equations (CHNS System). In this work, we study the well-posedness results for the CHNS system with…
In the framework of the nonsmooth critical point theory for lower semi-continuous functionals, we propose a direct variational approach to investigate the existence of infinitely many weak solutions for a class of semi-linear elliptic…
The authors of this paper deal with the existence and regularities of weak solutions to the homogenous $\hbox{Dirichlet}$ boundary value problem for the equation $-\hbox{div}(|\nabla u|^{p-2}\nabla u)+|u|^{p-2}u=\frac{f(x)}{u^{\alpha}}$.…
We consider linear boundary value problems for higher-order parameter-elliptic equations, where the boundary data do not belong to the classical trace spaces. We employ a class of Sobolev spaces of mixed smoothness that admits a generalized…
We study the local and global wellposedness of the initial-boundary value problem for the biharmonic Schr\"odinger equation on the half-line with inhomogeneous Dirichlet-Neumann boundary data. First, we obtain a representation formula for…
We study a superlinear elliptic boundary value problem involving the $p$-laplacian operator, with changing sign weights. The problem has positive solutions bifurcating from the trivial solution set at the two principal eigenvalues of the…
In this paper, we investigate the existence of weak solution for a Kirchhoff type problem driven by a nonlocal operator of elliptic type in a fractional Orlicz-Sobolev space, with homogeneous Dirichlet boundary conditions {\small$$…
Elliptic estimates in Hardy classes are proved on domains with minimally smooth boundary. The methodology is different from the original methods of Chang/Krantz/Stein.
We are concerned with the existence of infinitely many radial symmetric solutions for a nonlinear stationary problem driven by a new class of nonhomogeneous differential operators. Our proof relies on the symmetric version of the mountain…
We investigate existence and uniqueness of solutions to second-order elliptic boundary value problems containing a power nonlinearity applied to a fractional Laplacian. We detect the critical power separating the existence from the…
This work is concerned with the existence and multiplicity of solutions for the following class of quasilinear problems $$ -\Delta_{\Phi}u+\phi(|u|)u=f(u)~\text{in} ~\Omega_{\lambda}, u(x)>0 ~\text{in}~\Omega_{\lambda}, u=0~ \mbox{on}…
We establish new existence and non-existence results for positive solutions of the Einstein-scalar field Lichnerowicz equation on compact manifolds. This equation arises from the Hamiltonian constraint equation for the Einstein-scalar field…
Let us consider a semilinear boundary value problem $ - \Delta u= f(x,u),$ in $\Omega,$ with Dirichlet boundary conditions, where $ \Omega \subset \mathbb{R}^N $, $N> 2,$ is a bounded smooth domain. We provide sufficient conditions…