Related papers: On weak solutions for fourth-order problems involv…
We prove the existence of at least three weak solutions for the fourth-order problem with indefinite weight involving the Leray-Lions operator with nonstandard growth conditions. The proof of our main result uses variational methods and the…
In this paper, we consider the existence and uniqueness of weak solutions of a nonlinear elliptic equation with a variable exponent, a monotonic type operator and a convection term. With the topological degree theory, we prove the existence…
The Aubin-Lions lemma and its variants play crucial roles for the existence of weak solutions of nonlinear evolutionary PDEs. In this paper, we aim to develop some compactness criteria that are analogies of the Aubin--Lions lemma for the…
In this paper, we investigate weak solutions and Perron-Wiener-Brelot solutions to the linear stationary Kramers-Fokker-Planck equation in bounded domains. We establish the existence of weak solutions in product domains by applying the…
We study existence and regularity of weak solutions for the following PDE $$ -\dive(A(x,u)|\nabla u|^{p-2}\nabla u) = f(x,u),\;\;\mbox{in $B_1$}. $$ where $A(x,s) = A_+(x)\chi_{\{s>0\}}+A_-(x)\chi_{\{s\le 0\}}$ and $f(x,s) =…
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 consider a class of fourth order elliptic systems which include the Euler-Lagrange equations of biharmonic mappings in dimension 4 and we prove that weak limit of weak solutions to such systems is again a weak solution to a limit system.
The aim of this paper is investigating the existence and multiplicity of weak solutions to non--local equations involving the {\em magnetic fractional Laplacian}, when the nonlinearity is subcritical and asymptotically linear at infinity.…
In this paper, we draw on the ideas of [5] to extend the standard Serrin criterion [17] to an anisotropic version thereof. Because we work on weak solutions instead of strong ones, the functions involved have low regularity. Our method…
The global existence of weak solutions to a class of quasilinear parabolic equations with nonlinearities depending on first order terms and integrable data in a moving domain is investigated. The class includes the $p$-Laplace equation as a…
In this work we use variational methods to prove results on existence and concentration of solutions to a problem in $\mathbb{R}^N$ involving the $1-$Laplacian operator. A thorough analysis on the energy functional defined in the space of…
We study the optimization problem over the weakly Pareto set of a convex multiobjective optimization problem given by polynomial functions. Using Lagrange multiplier expressions and the weight vector, we give three types of representations…
In this paper, we investigate the existence and multiplicity of weak solutions to problems involving a superposition operator of the type $$\int_{[0, 1]}(- \Delta)^s u d \mu(s),$$ for a signed measure $\mu$ on the interval of fractional…
We prove an existence result for a class of Dirichlet boundary value problems with discontinuous nonlinearity and involving a Leray-Lions operator. The proof combines monotonicity methods for elliptic problems, variational inequality…
This work is devoted to the study of the existence of at least one weak solution to nonlocal equations involving a general integro-differential operator of fractional type. As a special case, we derive an existence theorem for the…
We investigate the multiplicity of nontrivial weak solutions for a class of complex equations. This class of problems are related with the existence of solitary waves for a nonlinear Sch\"{o}dinger equation. The main result is established…
In this paper, we consider a class of quasilinear stationary Kirchhoff type potential systems in unbounded domains, which involves a general variable exponent elliptic operator. Under some suitable conditions on the nonlinearities, we…
We prove the existence and multiplicity of weak solutions for a mixed local-nonlocal problem at resonance. In particular, we consider a not necessarily positive operator which appears in models describing the propagation of flames. A…
We consider the Neumann problem for the equation with the Vladimirov-Taibleson fractional differentiation operator over a non-Archimedean local field. We study weak solutions following the method by Dipierro, Ros-Oton and Valdinoci (2017).…
We prove existence of a bounded weak solution to a degenerate quasilinear subdiffusion problem with bounded measurable coefficients that may explicitly depend on time. The kernel in the involved integro-differential operator w.r.t. time…