Related papers: On sequences of solutions for discrete anisotropic…

We present new criteria on the existence of fixed points that combine some monotonicity assumptions with the classical fixed point index theory. As an illustrative application, we use our theoretical results to prove the existence of…

This paper establishes the existence of infinitely many solutions for nonlinear problems without any symmetry, achieving three major advances. First, in the setting of semilinear elliptic PDEs, we introduce a refined variational truncation…

In this note a critical point result for differentiable functionals is exploited in order to prove that a suitable class of one-dimensional fractional problems admits at least one non-trivial solution under an asymptotical behaviour of the…

The existence and multiplicity of positive periodic solutions for first non-autonomous singular systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter. The proof of our…

On the two dimensional sphere, we consider axisymmetric critical points of an isoperimetric problem perturbed by a long-range interaction term. When the parameter controlling the nonlocal term is sufficiently large, we prove the existence…

We obtain a comparison result for solutions to nonlinear fully anisotropic elliptic problems by means of anisotropic symmetrization. As consequence we deduce a priori estimates for norms of the relevant solutions.

We study the existence and multiplicity of positive solutions for a nonlinear fourth-order two-point boundary value problem. The approach is based on critical point theorems in conical shells, Krasnoselskii's compression-expansion theorem,…

Generally, natural scientific problems are so complicated that one has to establish some effective perturbation or nonperturbation theories with respect to some associated ideal models. In this Letter, a new theory that combines…

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…

This paper deals with the existence of solutions to a class of fourth order nonlinear elliptic equations. The technique used relies on critical points theory. The solutions appeared as critical points of a functional restricted to a…

In this article we study the asymptotic behavior, of the solution of a nonlinear elliptic, anisotropic singular perturbations problem in cylindrical domain, the limit problem is given and strong convergences are proved, we also give an…

We consider an anisotropic $(p,2)$-equation, with a parametric and superlinear reaction term. We show that for all small values of the parameter the problem has at least five nontrivial smooth solutions, four with constant sign and the…

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…

We consider a nonlinear Dirichlet problem driven by a variable exponent $p$-Laplacian plus an indefinite potential term. The reaction has the competing effects of a parametric concave (sublinear) term and of a convex (superlinear)…

The aim of this paper is to employ variational techniques and critical point theory to prove some conditions for the existence of solutions to nonlinear impulsive dynamic equation with homogeneous Dirichlet boundary conditions. Also we will…

Existence, uniqueness and stability of kinetic and entropy solutions to the boundary value problem for the Kolmogorov-type genuinely nonlinear ultra-parabolic equation with a smooth source term is established. After this, we consider the…

Using the theory of fixed point index, we discuss the existence and multiplicity of non-negative solutions of a wide class of boundary value problems with coupled nonlinear boundary conditions. Our approach is fairly general and covers a…

We deal with nonlinear systems of parabolic type satisfying component-wise structural conditions. The nonlinear terms are Carath\'eodory maps having controlled growth with respect to the solution and the gradient and the data are in…

A general sufficient condition for the convergence of subsequences of solutions of non-autonomous, nonlinear difference equations and systems is obtained. For higher order equations the delay sizes and patterns play essential roles in…

In this paper we consider a Dirichlet problem driven by an anisotropic $(p,q)$-differential operator and a parametric reaction having the competing effects of a singular term and of a superlinear perturbation. We prove a bifurcation-type…