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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]

In this paper, we study the existence of a Nash‐type equilibrium for a non‐potential nonlinear system by combining variational methods with the monotonicity approach. The advance over existing research is that we can consider systems of Dirichlet problems in which the operator is not necessarily linear. [ABSTRACT FROM AUTHOR]

We provide parameter‐dependent version of the Browder–Minty Theorem in case when the solution is unique utilizing different types of monotonicity and compactness assumptions related to condition (S)2. Potential equations and the convergence of their Euler action functionals are also investigated. Applications towards the dependence on parameters for both potential and nonpotenial nonlinear Dirichlet boundary problems are given. [ABSTRACT FROM AUTHOR]

We investigate the existence of variational generalized solutions to coercive competitive equations driven by a competing p , q − Laplacian type operator with weigth depending on the gradient. An abstract existence result based on a Galerkin scheme is therefore obtained and subsequently applied. [ABSTRACT FROM AUTHOR]

Using monotonicity methods, the Lagrange multiplier rule, and some variational arguments, we consider a type of localization results pertaining to the existence of critical points to action functionals on a closed ball. A variant of the Schechter critical point theorem on a ball in Hilbert and Banach spaces is obtained. Applications to nonlinear Dirichlet problem and to partial difference equations are given in the final part of this paper. [ABSTRACT FROM AUTHOR]

Using the global diffeomorphism theorem we consider the existence of solutions to the following Dirichlet problem,, whereis a jointly continuous function subject to some further growth conditions. Together with a given problem we consider the family of its discretizations and as a result we prove the existence of a non-spurious solution. [ABSTRACT FROM PUBLISHER]

In this note we consider Dirichlet boundary value problem on a half line. Using critical point theory we prove the existence of at least one nontrivial solution. [ABSTRACT FROM AUTHOR]

Using direct variational method we consider the existence of non-spurious solutions to the following Dirichlet problem,whereis a jointly continuous function convex inwhich does not need to satisfy any further growth conditions. [ABSTRACT FROM PUBLISHER]

In this paper we consider the Dirichlet problem for a discrete anisotropic equation with some function α a nonlinear term f, and a numerical parameter λ : Δ (α (k) |Δu(k - 1)|p(k - 1)-2 Δu(k - 1)) + λf(k, u(k)) = 0; k ∈ [1, T]. We derive the intervals of a numerical parameter λ for which the considered BVP has at least 1, exactly 1, or at least 2 positive solutions. Some useful discrete inequalities are also derived. [ABSTRACT FROM AUTHOR]

Abstract: We investigate the continuous dependence on parameters for the mountain pass solutions of second order discrete equations with -Laplacian and Dirichlet type boundary conditions. We show that assumptions leading to the existence of nontrivial solutions lead also to its continuous dependence on parameters. We investigate also the uniqueness of solutions. [Copyright &y& Elsevier]

Using mountain pass arguments and the Karsuh-Kuhn-Tucker Theorem, we prove the existence of at least two positive solution for anisotropic discrete Dirichlet boundary-value problems. Our results generalized and improve those in [16]. [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: Using a direct variational approach with no global growth conditions on the nonlinear term, we consider the existence of solutions and their dependence on a functional parameter for the fourth order Dirichlet problem connected with the elastic beam equation. We investigate also the existence of an optimal process for such an optimal control problem in which the dynamics is described by the beam equation. [ABSTRACT FROM AUTHOR]

Abstract: We begin with using a dual variational method in proving the existence of solutions to a beam equation with Dirichlet boundary conditions and with a non-monotone nonlinear term. Later we investigate the dependence on a control parameter for the state equation. We find the optimal process for the optimal control problem in which the dynamics is governed by the nonlinear beam equation. [Copyright &y& Elsevier]

Abstract: We consider the existence of solutions and the continuous dependence on a parameter results for fourth-order Dirichlet problem connected with the elastic beam equation. We introduce a dual variational method. [Copyright &y& Elsevier]

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 consider the existence of solutions to the Dirichlet problem [image omitted] in case the nonlinearity satisfies local growth conditions, where [image omitted] denotes the pseudo-Laplacian with p(x)-growth. We introduce a dual variational method and provide duality relations for both action and dual action functionals that later results in the necessary and sufficient conditions for the existence of a solution. Based on these results, we obtain a sufficient condition for stability of solutions. Finally, we show that certain optimal control problem with state constraints admits a solution. [ABSTRACT FROM AUTHOR]

We provide the existence and the stability results for higher order Dirichlet problems with convex nonlinearity which satisfies general local growth conditions. We construct a dual variational method and investigate relations between primal action functional and dual action functional. [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 study the stability and the solvability of a family of problems − (ϕ (x ′)) ′ = g (t , x , x ′ , u) + f * with Dirichlet boundary conditions, where ϕ , u, f * are allowed to vary as well. Applications for boundary value problems involving the p-Laplacian operator are highlighted. [ABSTRACT FROM AUTHOR]

Using the direct variational method together with the monotonicity approach we consider the existence of non-spurious solutions to the following Dirichlet problem − x ¨ t   = f t , x t , x 0   = x 1   = 0 , where f :   0 , 1   ×   R → R is a jointly continuous and not necessarily convex function. A new approach towards deriving the discrete family of approximating problems is proposed. [ABSTRACT FROM AUTHOR]