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Quaestiones Mathematicae, ISSN 1607-3606, 08/2016, Volume 39, Issue 5, pp. 683 - 688
We provide sufficient conditions for a mapping f : R n → R n to be a global diffeomorphism in case f need not be continuously differentiable. Instead it is... 
Global diffeomorphism | local diffeomorphism | mountain pass lemma | non-smooth critical point theory | inverse function
Journal Article
Results in Mathematics, ISSN 1422-6383, 12/2019, Volume 74, Issue 4, pp. 1 - 13
We investigate the continuous dependence on parameters for the mountain pass solutions of second order elliptic equations with Dirichlet type boundary... 
35J20 | Mathematics, general | Mathematics | 35R02 | MATHEMATICS | MATHEMATICS, APPLIED | SYSTEMS
Journal Article
Taiwanese Journal of Mathematics, ISSN 1027-5487, 10/2016, Volume 20, Issue 5, pp. 1079 - 1092
We investigate the existence of at least two nontrivial solutions to a Dirichlet problem on the Sierpinski gasket. We develop some general abstract... 
Mathematical theorems | Gaskets | Critical points | Dirichlet problem | Mountain passes | Fractals | Mathematics | Laplacians | Convexity | Nontrivial solutions | Sierpinski gasket | Elliptic equation | Multiplicity | Fenchel-Young duality | MOUNTAIN PASS | MATHEMATICS | FRACTALS | THEOREM | SETS | EQUATIONS | SPECTRUM
Journal Article
Taiwanese Journal of Mathematics, ISSN 1027-5487, 10/2015, Volume 19, Issue 5, pp. 1495 - 1508
Using the Fenchel-Young duality and mountain pass geometry we derive a new multiple critical point theorem. In a finite dimensional setting it becomes three... 
Mountain passes | Boundary value problems | Mathematical theorems | Banach space | Critical points | Critical point | P(x)–Laplacian | Discrete p(k)–Laplacian | Fenchel-Young transform | Multiplicity | LAPLACIAN | MATHEMATICS | p(x)-Laplacian | DISCRETE P(.)-LAPLACIAN | VARIATIONAL PRINCIPLE | GROWTH | Discrete p(k)-Laplacian | EQUATIONS | NEUMANN PROBLEMS
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 04/2016, Volume 39, Issue 6, pp. 1480 - 1492
In this note, a critical point result for differentiable functionals is exploited in order to prove that a suitable class of one‐dimensional fractional... 
variational methods | fractional problems | existence results | ORDER | MATHEMATICS, APPLIED | LAPLACE EQUATION | POSITIVE SOLUTIONS | BOUNDARY-VALUE-PROBLEMS | DIFFERENTIAL-EQUATIONS | OPERATORS | Concretes | Nonlinearity | Critical point | Functionals | Asymptotic properties | Mathematical analysis
Journal Article
Journal of Difference Equations and Applications, ISSN 1023-6198, 02/2018, Volume 24, Issue 2, pp. 277 - 290
Using the global diffeomorphism theorem we consider the existence of solutions to the following Dirichlet problem , , where is a jointly continuous function... 
34B15 | Global diffeomorphism | discrete boundary value problem | non-spurious solution | 39A12 | Palais-Smale condition | Palais–Smale condition | MATHEMATICS, APPLIED | NONSPURIOUS SOLUTIONS | Dirichlet problem | Theorems | Boundary value problems | Existence theorems | Continuity (mathematics)
Journal Article
Opuscula Mathematica, ISSN 1232-9274, 2019, Volume 39, Issue 2, pp. 131 - 144
In this work we consider second order Dirichelet boundary value problem with nonlinearity depending on the derivative. Using a global diffeomorphism theorem we... 
Diffeomorphism | Non-potential problems | Variational methods | Palais-Smale condition | Monotone methods | Uniqueness | variational methods | non-potential problems | palais-smale condition | monotone methods | uniqueness | diffeomorphism
Journal Article
Mechatronics, ISSN 0957-4158, 08/2016, Volume 37, pp. 21 - 32
•Description of spectrum-based modal parameters identification with Particle Swarm Optimization (smiPSO) algorithm.•Results compared to other known modal... 
Vibrations | Identification | Modal analysis | Artificial Intelligence | Particle Swarm Optimization | ROBOTICS | ALGORITHM | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, MECHANICAL | ENGINEERING, ELECTRICAL & ELECTRONIC | Mathematical optimization | Damping | Mechatronics | Algorithms | Resonant frequency | Paper | Swarm intelligence | Mechanical systems | Artificial intelligence
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 2011, Volume 218, Issue 4, pp. 1247 - 1253
We investigate the dependence on parameters for the discrete boundary value problem connected with the Emden–Fowler equation. A variational method is used in... 
Variational method | Dependence on parameters | Discrete Emden–Fowler equation | Coercivity | Discrete Emden-Fowler equation | EXISTENCE | MATHEMATICS, APPLIED | MULTIPLE SOLUTIONS | BOUNDARY-VALUE-PROBLEMS | Boundary value problems | Mathematical models | Variational methods | Computation | Mathematical analysis
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 2011, Volume 218, Issue 7, pp. 3954 - 3956
We undertake the question of the multiplicity of solutions to the discrete Emden–Fowler BVP by correcting some results contained in [2]. 
Multiplicity of solutions | Discrete boundary value problem | Variational method | EXISTENCE | BOUNDARY-VALUE-PROBLEMS | MATHEMATICS, APPLIED | Boundary value problems | Mathematical models | Difference equations | Computation | Mathematical analysis
Journal Article
Quaestiones Mathematicae, ISSN 1607-3606, 05/2018, Volume 41, Issue 4, pp. 515 - 528
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 global inversion theorem | Mountain pass theorem | locally Lipschitz function | global implicit function | MATHEMATICS | MULTIPLE SOLUTIONS | HOMEOMORPHISM
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 11/2016, Volume 290, pp. 376 - 391
We use the direct variational method, the Ekeland variational principle, the mountain pass geometry and Karush–Kuhn–Tucker theorem in order to investigate... 
Critical point theory | Existence and multiplicity | Weighted graph | [formula omitted]Laplacian on a graph | p(·)− Laplacian on a graph | MATHEMATICS, APPLIED | P-LAPLACIAN | GROWTH | EQUATIONS | NEUMANN PROBLEMS | P(.)-LAPLACIAN | p(center dot)-Laplacian on a graph
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 2011, Volume 24, Issue 12, pp. 2015 - 2018
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... 
Nonlinear system | Variational method | Duality | MATHEMATICS, APPLIED | PARAMETER | Nonlinear dynamics | Boundary value problems | Difference equations | Variational methods | Mathematical analysis | Dirichlet problem | Nonlinearity | Dynamical systems
Journal Article
Journal of Difference Equations and Applications, ISSN 1023-6198, 09/2012, Volume 18, Issue 9, pp. 1607 - 1610
Using the direct method of the calculus of variations, we investigate the existence, uniqueness and continuous dependence on parameters for solutions of... 
existence | anisotropic problem | continuous dependence on parameters | discrete boundary value problem | uniqueness | MATHEMATICS, APPLIED | BOUNDARY-VALUE-PROBLEMS | Boundary value problems | Difference equations | Anisotropy | Mathematical analysis | Uniqueness | Boundary conditions | Dirichlet problem | Well posed problems
Journal Article
Electronic Journal of Differential Equations, 2018, Volume 2018, Issue 25, pp. 87 - 102
Journal Article
Studia Scientiarum Mathematicarum Hungarica, ISSN 0081-6906, 03/2014, Volume 51, Issue 1, pp. 17 - 23
Applying certain convexity arguments we investigate the existence of a classical solution for a Dirichlet problem for which the Euler action functional is not... 
Dirichlet Problem | coercivity | 58E30 | Fenchel-Young conjugate | Primary 34B15 | MATHEMATICS | Dirichlet problem | Convexity | Gateaux | Mathematical analysis | Coercive force
Journal Article
Electronic Journal of Qualitative Theory of Differential Equations, ISSN 1417-3875, 2018, Volume 2018, Issue 12, pp. 1 - 12
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... 
Critical point | Mountain pass | Dirichlet boundary value problem | Half line | MATHEMATICS | critical point | MATHEMATICS, APPLIED | half line | mountain pass | dirichlet boundary value problem
Journal Article
Journal of Difference Equations and Applications, ISSN 1023-6198, 07/2012, Volume 18, Issue 7, pp. 1253 - 1256
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. 
continuous dependence on parameters | nonlinear system | discrete boundary value problem | strongly monotone principle | EXISTENCE | MATHEMATICS, APPLIED | BOUNDARY-VALUE-PROBLEMS
Journal Article
Journal of Difference Equations and Applications, ISSN 1023-6198, 10/2011, Volume 17, Issue 10, pp. 1441 - 1453
Journal Article
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