Related papers: Nodal and multiple solutions for a nonhomogeneous …
We derive local asymptotics of solutions to second order elliptic equations at the edge of a $(N-1)$-dimensional crack, with homogeneous Neumann boundary conditions prescribed on both sides of the crack. A combination of blow-up analysis…
We prove an existence theorem for positive solutions to Lichnerowicz-type equations on complete manifolds with boundary and nonlinear Neumann conditions. This kind of nonlinear problems arise quite naturally in the study of solutions for…
The main purpose of this paper is to study the existence of least energy sign-changing solutions for Logarithmic weighted $(N,p)$-Laplacian problem in the unit ball $B$ of $\mathbb{R}^{N},$ $N>2$. The non-linearity of the equation is…
The aim of this paper is to extend previous results regarding the multiplicity of solutions for quasilinear elliptic problems with critical growth to the variable exponent case. We prove, in the spirit of \cite{DPFBS}, the existence of at…
We prove the existence of solutions for a class of quasilinear problems involving variable exponents and with nonlinearity having critical growth. The main tool used is the variational method, more precisely, Ekeland's Variational Principle…
We present a nonvariational setting for the Neumann problem for the Poisson equation for solutions that are H\"{o}lder continuous and that may have infinite Dirichlet integral. We introduce a distributional normal derivative on the boundary…
We provide a general approach to the classification results of stable solutions of (possibly nonlinear) elliptic problems with Robin conditions. The method is based on a geometric formula of Poincar\'e type, which is inspired by a classical…
We consider a parametric semilinear Robin problem driven by the Laplacian plus an indefinite and unbounded potential. In the reaction, we have the competing effects of a concave term appearing with a negative sign and of an asymmetric…
We consider the following problem $$(P) \begin{cases} -\Delta_{p}u= c(x)|u|^{q-1}u+\mu |\nabla u|^{p}+h(x) & \ \ \mbox{ in }\Omega, u=0 & \ \ \mbox{ on } \partial\Omega, \end{cases}$$ where $\Omega$ is a bounded set in $\mathbb{R}^{N}$…
It is shown that the non-homogeneous Dirichlet and Neuman problems for the $2^{nd}$-order Seiberg-Witten equation admit a regular solution once the $\mathcal{H}$-condition (described in the article) is satisfied. The approach consist in…
In this paper by exploiting critical point theory, the existence of two distinct nontrivial solutions for a nonlinear algebraic system with a parameter is established. Our goal is achieved by requiring an appropriate behavior of the…
In this article, we focus on a doubly nonlinear nonlocal parabolic initial boundary value problem driven by the fractional $p$-Laplacian equipped with homogeneous Dirichlet boundary conditions on a domain in $\mathbb{R}^{d}$ and composed…
In this paper we study an equation driven by a nonlocal anisotropic operator with homogeneous Dirichlet boundary conditions. We find at least three non trivial solutions: one positive, one negative and one of unknown sign, using variational…
We study a nonlinear Neumann boundary value problem associated to a nonhomogeneous differential operator. Taking into account the competition between the nonlinearity and the bifurcation parameter, we establish sufficient conditions for the…
Existence of a generalized solution to a strongly singular convective elliptic equation in the whole space is established. The differential operator, patterned after the (p,q)-Laplacian, can be non-homogeneous. The result is obtained by…
We propose a new variational approach to finding multiple critical points for strongly indefinite problems without assuming the weak upper semicontinuity on the variational functionals. By this approach, we obtain the existence of…
The purpose of this paper is to investigate the existence of three different weak solutions to a nonlinear elliptic problem that is governed by the weighted {\varphi}-Laplacian operator and subjected to Dirichlet boundary conditions. We…
This paper investigates the regularity of solutions and structural properties of the free boundary for a class of fourth-order elliptic problems with Neumann-type boundary conditions. The singular and degenerate elliptic operators studied…
We study the existence of nontrivial solutions for a nonlinear fractional elliptic equation in presence of logarithmic and critical exponential nonlinearities. This problem extends [5] to fractional $N/s$-Laplacian equations with…
We show that all Lie point symmetries of various classes of nonlinear differential equations involving critical nonlinearities are variational/divergence symmetries.