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We investigate fourth‐order equations with Dirichlet‐type boundary conditions with perturbation unbounded from above making the problem non‐potential. We apply variational method to some auxiliary problem and conclude about the existence and uniqueness to the original one. Multiple solutions are also considered. We conclude our note with the result pertaining to the continuous dependence on parameters. [ABSTRACT FROM AUTHOR]

Using the variational approach, we investigate the existence of solutions and their dependence on functional parameters for classical solutions to the second order impulsive boundary value Dirichlet problems with L1 right hand side. [ABSTRACT FROM AUTHOR]

In this paper we investigate the existence of solutions to impulsive problems with a p( t)-Laplacian and Dirichlet boundary value conditions. We introduce two types of solutions, namely a weak and a classical one which coincide because of the fundamental lemma of the calculus of variations. Firstly we investigate the existence of solution to the linear problem, i.e. a problem with a fixed rigth hand side. Then we use a direct variational method and next a mountain pass approach in order to get the existence of at least one weak solution to the nonlinear problem. [ABSTRACT FROM AUTHOR]

Abstract: We derive a dual variational method in order to obtain the existence of a bounded solution to a certain nonlinear system with non-monotone nonlinearities. We consider such a system representing a difference equation arising from evaluating some Dirichlet boundary value problems. [Copyright &y& Elsevier]

Abstract: We investigate the dependence on parameters for the discrete boundary value problem connected with the Emden–Fowler equation. A variational method is used in order to obtain a general scheme allowing for investigating the dependence on parameters of discrete boundary value problems. [Copyright &y& Elsevier]

We investigate the dependence on parameters for second-order difference equations with two-point boundary value conditions using a variational method in case when the corresponding Euler action functional is coercive. Some applications for discrete Emden-Fowler equation are also given. [ABSTRACT FROM AUTHOR]

We improve the results of Li by using less restrictive assumptions. [ABSTRACT FROM AUTHOR]

Using critical point theory and some monotonicity results we consider the existence of solutions to a boundary value problem connected with the discrete elliptic equation with a positive parameter. [ABSTRACT FROM AUTHOR]

We apply the dual variational method in order to prove that a certain system of difference equations with a parameter has at least one nontrivial bounded solution. [ABSTRACT FROM AUTHOR]

Abstract: We show the existence and stability of solutions for a family of Dirichlet problems in a bounded domain and with nonconvex nonlinearity satisfying some local growth conditions. The conditions upon V and L allow for considering the -Laplacian equation. We use the relations between critical points and critical values to the primal and a suitable dual action functional to get the existence, stability and some properties of the solutions. [Copyright &y& Elsevier]

We provide existence results for an operator equation [image omitted] where Λ ∇AΛ*:V → V* is a nonlinear monotone operator, V ⊂ H ⊂ V* is Gelfand triple, and ∇F:H → H is a gradient mapping. We introduce an abstract version of the dual variational method. The solution is obtained as the limit of the minimizing sequence whose existence and convergence is proved. We consider stability of solutions to a given problem with respect to a parameter. Examples are given. [ABSTRACT FROM AUTHOR]

Abstract: We show the existence and stability of solutions for a family of Dirichlet problems with nonlinearity satisfying some local growth conditions. We construct a new duality theory which differs from the known ones in that it does not require a type of a Palais–Smale condition. [Copyright &y& Elsevier]

Abstract: We study the existence of solutions, their stability and numerical approximations for elliptic Dirichlet problems with some general growth conditions. We consider an abstract family of equations for which we derive a new variational method to obtain existence and stability results which a further applied to concrete problems. Galerkin type approximations are also obtained. [Copyright &y& Elsevier]

We provide a duality theory and existence results for a superlinear operator equation Δ T(x) = Δ N (x). We use the abstract version of the so called dual variational method. The solution is obtained as a limit of a minimizng sequence whose existence and convergence is proved. [ABSTRACT FROM AUTHOR]

Abstract: We undertake the question of the multiplicity of solutions to the discrete Emden–Fowler BVP by correcting some results contained in . [Copyright &y& Elsevier]