Series S of Discrete and Continuous Dynamical Systems only publishes theme issues.Each issue is devoted to a specific area of the mathematical, physical andengineering sciences. This area will define a research frontier that isadvancing rapidly, often bridging mathematics and sciences. DCDS-S isessential reading for mathematicians, physicists, engineers and otherphysical scientists. The journal is published bimonthly.
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The aim of this paper is to prove a reverse Hölder inequality for nonnegative adjoint solutions for elliptic operator in non divergence form in
arises naturally as the formal adjoint of the operator in "non divergence form"
The reason to study the solutions of the adjoint operator is that they are not only important for the solvability of
We are concerned with the existence of nontrivial weak solutions for a class of generalized minimal surface equations with subcritical growth and Dirichlet boundary condition. In relationship with the values of several variable exponents, we establish two sufficient conditions for the existence of solutions. In the first part of this paper, we prove the existence of a non-negative solution. Next, we are concerned with the existence of infinitely many solutions in a symmetric abstract setting.
In this paper we discuss the existence and non-existence of weak solutions to parametric fractional equations involving the square root of the Laplacian
The existence of at least two non-trivial
We consider the following singular semilinear problem
The goal of the paper is to investigate the existence of solutions for semilinear upper diagonal infinite systems of differential equations. We will look for solutions of the mentioned infinite systems in a Banach tempered sequence space. In our considerations we utilize the technique associated with the Hausdorff measure of noncompactness and some existence results from the theory of ordinary differential equations in abstract Banach spaces.
We consider solutions
We consider the boundary value problem associated to the curl operator, with vanishing Dirichlet boundary conditions. We prove, under mild regularity of the data of the problem, existence of classical solutions.
The Leray-Lions operators are versatile enough to be particularized to various elliptic operators, so they receive a lot of attention. This paper introduces to the mathematical literature Leray-Lions type operators that are appropriate for the study of the variable exponent problems of higher order. We establish some properties concerning these general operators and then we apply them to a fourth order problem with variable exponents.
In this note we exploit nonlinear capacity estimates in the spirit of Mitidieri-Pohozaev [
We are interested in the regularity of local minimizers of energy integrals of the Calculus of Variations. Precisely, let
In this paper we prove an existence theorem for positive solutions of a nonlinear Dirichlet problem involving the p-Laplacian operator on a smooth bounded domain when a nonlinearity depending on the gradient is considered. Our main theorem extends a previous result by Ruiz in [
We consider a nonlinear elliptic equation with Robin boundary condition driven by the p-Laplacian and with a reaction term which depends also on the gradient. By using a topological approach based on the Leray-Schauder alternative principle, we show the existence of a smooth solution.
We study the system
In this article, we study the following parabolic equation involving the fractional Laplacian with singular nonlinearity
We consider a nonlinear nonhomogeneous Dirichlet problem driven by the sum of a
The paper is focused on existence of nontrivial solutions of a Schrödinger-Hardy system in the Heisenberg group, involving critical nonlinearities. Existence is obtained by an application of the mountain pass theorem and the Ekeland variational principle, but there are several difficulties arising in the framework of Heisenberg groups, also due to the presence of the Hardy terms as well as critical nonlinearities.
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. The proof relies on the symmetric version of the mountain pass theorem.
The aim of this paper is to discuss the existence and multiplicity of solutions for the following fractional
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