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1
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New variational principle and duality for an abstract semilinear Dirichlet problem

100%
Galewski M.
Annales Polonici Mathematici
|
2003
|
tom 82
|
nr 1
51-60
EN
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.
2
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Stability of solutions for an abstract Dirichlet problem

100%
Galewski M.
Annales Polonici Mathematici
|
2004
|
tom 83
|
nr 3
273-280
EN
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.
3
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On variational impulsive boundary value problems

100%
Galewski M.
Open Mathematics
|
2012
|
tom 10
|
nr 6
1969-1980
EN
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.
4
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Corrections to "Existence and stability of solutions for semilinear Dirichlet problems" (Ann. Polon. Math. 88 (2006), 127-139)

100%
Galewski M.
Annales Polonici Mathematici
|
2008
|
tom 93
|
nr 2
197-198
5
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Existence and stability of solutions for semilinear Dirichlet problems

100%
Galewski M.
Annales Polonici Mathematici
|
2006
|
tom 88
|
nr 2
127-139
EN
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.
6
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Continuous dependence on parameters for second order discrete BVP’s

64%
Galewski M., Głąb S.
Open Mathematics
|
2012
|
tom 10
|
nr 3
1076-1083
EN
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.
7
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Three solutions to discrete anisotropic problems with two parameters

64%
Galewski M., Kowalski P.
Open Mathematics
|
2014
|
tom 12
|
nr 10
1403-1415
EN
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.
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