Related papers: Super critical problems with concave and convex no…

In this paper we study a general class of nonlinear elliptic problems in divergence form. First, we prove that the solutions to these problems satisfy a convexity property when the given domain is strictly convex. Then, making use of this…

We consider the most general class of linear boundary-value problems for higher-order ordinary differential systems whose solutions and right-hand sides belong to the corresponding Sobolev spaces. For parameter-dependent problems from this…

This paper deals with the qualitative analysis of solutions to the following $(p,q)$-fractional equation: \begin{equation*} \begin{array}{rllll} (-\Delta)^{s_1}_{p}u+(-\Delta)^{s_2}_{q}u+V(x) \big(|u|^{p-2}u+|u|^{q-2}u\big) =…

In this paper, we investigate the following elliptic system with Sobolev critical growth $-\Delta u+P(|y'|,y'')u=u^{2^*-1}+\frac{\beta}{2} u^{\frac{2^*}{2}-1}v^{\frac{2^*}{2}},\ y\in R^N$, $-\Delta v+Q(|y'|,y'')v=v^{2^*-1}+\frac{\beta}{2}…

In this paper we study logarithmic double phase problems with variable exponents involving nonlinearities that have generalized critical growth. We first prove new continuous and compact embedding results in order to guarantee the…

In this paper we prove unique continuation principles for some systems of elliptic partial differential equations satisfying a suitable superlinearity condition. As an application, we obtain nonexistence of nontrivial (not necessarily…

We consider the wave equation with an energy supercritical focusing nonlinearity in general odd dimensions. We prove that any radial solution that remains bounded in the critical Sobolev space is global and scatters to a linear solution.

In this paper we present some very recent results regarding existence, uniqueness, and multiplicity of solutions for quasilinear elliptic equations and systems, exhibiting both singular and convective reaction terms. The importance of…

We study fourth-order quasilinear elliptic problems that involve the p-biharmonic operator and Navier boundary conditions. The nonlinear term grows at the critical Sobolev rate. Starting from a Hamiltonian system of two second-order…

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…

Using a method developped in [1] and [2], we prove the existence of weak non trivial solutions to fourth order elliptic equations with singularities and with critical Sobolev growth.

This paper develops a novel approach to necessary optimality conditions for constrained variational problems defined in generally incomplete subspaces of absolutely continuous functions. Our approach involves reducing a variational problem…

We prove new multiplicity results for some nonlocal critical growth elliptic equations in homogeneous fractional Sobolev spaces. The proofs are based on an abstract critical point theorem based on the ${\mathbb Z}_2$-cohomological index and…

Using some nonlinear domain decomposition method, we prove the existence of singular limits for solution of semilinear elliptic problems with exponential nonlinearity.

We are interested in regularity properties of semi-stable solutions for a class of singular semilinear elliptic problems with advection term defined on a smooth bounded domain of a complete Riemannian manifold with zero Dirichlet boundary…

In the paper we show that critical sequences associated with the mountain pass level for semilinear elliptic problems on $\R^N$ converge when the non-linearity is subcritical, superlinear and satisfies the penalty condition…

We show the existence of a weak solution of a semilinear elliptic Dirichlet problem on an arbitrary open set. We make no assumptions about the open set, very mild regularity assumptions on the semilinearity, plus a coerciveness assumption…

n this paper, we prove existence of nodal solutions for singular semilinear elliptic systems without variational structure where its both components are of sign changing. Our approach is based on sub-supersolutions method combined with…

In this paper, we prove the existence and regularity of weak positive solutions for a class of nonlinear elliptic equations with a singular nonlinearity, lower order terms and $L^{1}$ datum in the setting of variable exponent Sobolev…

We consider elliptic problems with nonclassical boundary conditions that contain additional unknown functions on the border of the domain of the elliptic equation and also contain boundary operators of higher orders with respect to the…