On the nonlinear elastic simply supported beam equation.
On variational impulsive boundary value problems
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.
On the Existence of Solutions for Abstract Nonlinear Operator Equations
We provide a duality theory and existence results for a operator equation where is not necessarily a monotone operator. 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.
New variational principle and duality for an abstract semilinear Dirichlet problem
A new variational principle and duality for the problem Lu = ∇G(u) are provided, where L is a positive definite and selfadjoint operator and ∇G is a continuous gradient mapping such that G satisfies superquadratic growth conditions. The results obtained may be applied to Dirichlet problems for both ordinary and partial differential equations.
Corrections to "Existence and stability of solutions for semilinear Dirichlet problems" (Ann. Polon. Math. 88 (2006), 127-139)
Existence and stability of solutions for semilinear Dirichlet problems
We provide existence and stability results for semilinear Dirichlet problems with nonlinearities satisfying some general local growth conditions. We derive a general abstract result which we then apply to prove the existence of solutions, their stability and continuous dependence on parameters for a sixth order ODE with Dirichlet type boundary data.
Stability of solutions for an abstract Dirichlet problem
We consider continuous dependence of solutions on the right hand side for a semilinear operator equation Lx = ∇G(x), where L: D(L) ⊂ Y → Y (Y a Hilbert space) is self-adjoint and positive definite and G:Y → Y is a convex functional with superquadratic growth. As applications we derive some stability results and dependence on a functional parameter for a fourth order Dirichlet problem. Applications to P.D.E. are also given.
Three solutions to discrete anisotropic problems with two parameters
In this note we derive a type of a three critical point theorem which we further apply to investigate the multiplicity of solutions to discrete anisotropic problems with two parameters.
Continuous dependence on parameters for second order discrete BVP’s
Using Fan’s Min-Max Theorem we investigate existence of solutions and their dependence on parameters for some second order discrete boundary value problem. The approach is based on variational methods and solutions are obtained as saddle points to the relevant Euler action functional.
On the existence and the stability of solutions for higher-order semilinear Dirichlet problems
We investigate the existence and stability of solutions for higher-order two-point boundary value problems in case the differential operator is not necessarily positive definite, i.e. with superlinear nonlinearities. We write an abstract realization of the Dirichlet problem and provide abstract existence and stability results which are further applied to concrete problems.
–convex transformability in nonlinear programming problems
We show that for -convex transformable nonlinear programming problems the Karush-Kuhn-Tucker necessary optimality conditions are also sufficient and we provide a method of solving such problems with the aid of associated -convex ones.
Impulsive boundary value problems for -Laplacian’s via critical point theory
In this paper we investigate the existence of solutions to impulsive problems with a -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...
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