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We show that the monotonicity methods can also be applied in the fractal setting to examine existence and also existence and uniqueness. Furthermore, we investigate the continuous dependence on parameters for the problem under consideration. [ABSTRACT FROM AUTHOR]

We prove a non-smooth generalization of the global implicit function theorem. More precisely we use the non-smooth local implicit function theorem and the non-smooth critical point theory in order to prove a non-smooth global implicit function theorem for locally Lipschitz functions. A comparison between several global inversion theorems is discussed. Applications to algebraic equations are given. [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]

We provide sufficient conditions for a mappingf:Rn → Rnto be a global diffeomorphism in casefneed not be continuously differentiable. Instead it is assumed to be strictly (Hadamard-like) and Fréchet differentiable. We use classical local invertibility conditions together with the non-smooth critical point theory. [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 work we investigate multiple solutions to discrete inclusions with the-Laplacian problem. We focus on the existence of three solutions with the aid of linking arguments and a new non-smooth three critical points tool, which we provide. [ABSTRACT FROM AUTHOR]

We discuss the eigenvalue problem for n-th order equations with multipoint boundary conditions. We present the variational method in spite of the fact that the nonlinearity is dependent on the derivative of n/2 order. The results can be applied applied to both sublinear and superlinear cases. [ABSTRACT FROM AUTHOR]

We investigate the existence of solutions of the system of anisotropic discrete boundary value problems using critical point theory. We apply direct variational approach, the Ky Fan min–max inequality and the mountain pass lemma. [ABSTRACT FROM AUTHOR]

Using the direct method of the calculus of variations, we investigate the existence, uniqueness and continuous dependence on parameters for solutions of second-order discrete anisotropic equations with Dirichlet boundary conditions. [ABSTRACT FROM PUBLISHER]

Using monotonicity theory, we investigate the continuous dependence on parameters for the discrete BVPs, which can be written in a form of a nonlinear system. [ABSTRACT FROM AUTHOR]

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]

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]

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]

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]

We provide definition of such a Fenchel–Young type duality for an invex function f that its second dual is a given function f. [ABSTRACT FROM AUTHOR]