Related papers: A Berestycki-Lions type result and applications
In this paper we show an abstract theorem that can be used to prove the existence of solution for a class of elliptic equation considered in Berestycki-Lions \cite{berest} and related problems. Moreover, we use the abstract theorem to show…
A fourth-order elliptic problem of Leray-Lions type is considered for combined nonlinearities and Sobolev-critical growth with Navier and Dirichlet boundary conditions. By combining variational methods and critical point theory, the…
We prove an abstract critical point theorem based on a cohomological index theory that produces pairs of nontrivial critical points with nontrivial higher critical groups. This theorem yields pairs of nontrivial solutions that are neither…
In this work we study the existence of nontrivial solution for the following class of semilinear degenerate elliptic equations $$ -\Delta_{\gamma} u + a(z)u = f(u) ~~ \mbox{in} ~~ \mathbb{R}^{N}, $$ where $\Delta_{\gamma}$ is known as the…
In this paper, we show the existence of a nontrivial weak solution for a nonlinear problem involving the fractional $p$-Laplacian operator and a Berestycki-Lions type nonlinearity. This solution satisfies a Pohozaev identity. Moreover, we…
Some existence results for a parametric Dirichlet problem defined on the Sierpi\'nski fractal are proved. More precisely, a critical point result for differentiable functionals is exploited in order to prove the existence of a well…
We introduce a new fixed point theorem of Krasnoselskii type for discontinuous operators. As an application we use it to study the existence of positive solutions of a second-order differential problem with separated boundary conditions and…
In this paper we prove a Lions type result for a large class of Orlicz-Sobolev space that can be nonreflexive and use this result to show the existence of solution for a large class of quasilinear problem on a nonreflexive Orlicz-Sobolev…
We consider critical points of a class of functionals on compact four-dimensional manifolds arising from Regularized Determinants for conformally covariant operators, whose explicit form was derived in [10], extending Polyakov's formula.…
We establish some existence results for a class of critical $N$-Laplacian problems in a bounded domain in ${\mathbb R}^N$. In the absence of a suitable direct sum decomposition, we use an abstract linking theorem based on the ${\mathbb…
We consider a functional being a difference of two differentiable convex functionals on a closed ball. Existence and multiplicity of critical points is investigated. Some applications are given.
We prove an existence result of weak solutions $u\in W_{0}^{1,p}\left( \Omega \right) \cap W_{\mathrm{loc}}^{1,q}\left( \Omega \right) $, to a Dirichlet problem for a second order elliptic equation in divergence form, under general and…
Consider the nonlinear scalar field equation \begin{equation} \label{a1} -\Delta{u}= f(u)\quad\text{in}~\mathbb{R}^N,\qquad u\in H^1(\mathbb{R}^N), \end{equation} where $N\geq3$ and $f$ satisfies the general Berestycki-Lions conditions. We…
In this paper, we present a novel approach to investigate the existence of multiple critical points for a class of nonsmooth functionals. This method provides a robust framework to analyze the existence of solutions for problems involving…
This paper concerns a nonlinear elliptic equation involving a critical Sobolev growth and a lower-order term. Under a Lions's condition, we prove the existence of at least one positive solution. Our approach consists in constructing a…
In this paper we prove a multiplicity result concerning the critical points of a class of functionals involving local and nonlocal nonlinearities. We apply our result to the nonlinear Schrodinger-Maxwell system and to the nonlinear elliptic…
We give a constructive proof of the classical Cauchy-Kovalevskaya theorem in the ODE setting which provides a sufficient condition for an initial value problem to have a unique analytic solution. Our proof is inspired by a modern functional…
An abstract linking result for Cerami sequences is proved without the Cerami condition. It is applied directly in order to prove the existence of critical points for a class of indefinite problems in infinite dimensional Hilbert Spaces. The…
We prove a unified and general criterion for the uniqueness of critical points of a functional in the presence of constraints such as positivity, boundedness, or fixed mass. Our method relies on convexity properties along suitable paths and…
We establish an abstract critical point theorem for locally Lipschitz functionals that does not require any compactness condition of Palais-Smale type. It generalizes and unifies three other critical point theorems established in…