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1
Content available On unique solvability of a Dirichlet problem with nonlinearity depending on the derivative
Bełdziński Michał, Galewski Marek
Opuscula Mathematica
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2019
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Vol. 39, no. 2
131-144
EN
In this work we consider second order Dirichelet boundary value problem with nonlinearity depending on the derivative. Using a global diffeomorphism theorem we propose a new variational approach leading to the existence and uniqueness result for such problems.
2
Content available Existence and multiplicity of solutions for a nonhomogeneous Neumann boundary problem
Klimczak L.
Opuscula Mathematica
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2015
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Vol. 35, no. 6
889--905
EN
We consider a nonlinear Neumann elliptic equation driven by a p-Laplacian-type operator which is not homogeneous in general. For such an equation the energy functional does not need to be coercive, and we use suitable variational methods to show that the problem has at least two distinct, nontrivial smooth solutions. Our formulation incorporates strongly resonant equations.
3
Content available remote Existence of solutions for higher order BVP with parameters via critical point theory
Jurkiewicz M., Przeradzki B.
Demonstratio Mathematica
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2015
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Vol. 48, nr 1
53--61
EN
This paper is concerned with the existence of at least one solution of the nonlinear 2k-th order BVP. We use the Mountain Pass Lemma to get an existence result for the problem, whose linear part depends on several parameters.
4
Content available remote Existence Result for Differential Inclusion with p(x) - Laplacian
Barnaś S.
Schedae Informaticae
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2012
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Vol. 21
41--54
EN
In this paper we study the nonlinear elliptic problem with p(x)- Laplacian (hemivariational inequality). We prove the existence of a nontrivial solution. Our approach is based on critical point theory for locally Lipschitz functionals due to Chang [4].
5
Content available remote Existence and Multiplicity of Solutions for Noncoercive Neumann Problems with p-Laplacian
Gasiński L., Papageorgiou N. S.
Schedae Informaticae
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2012
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Vol. 21
27--40
EN
We consider a nonlinear Neumann elliptic equation driven by the p-Laplacian and a Caratheodory perturbation. The energy functional of the problem need not be coercive. Using variational methods we prove an existence theorem and a multiplicity theorem, producing two nontrivial smooth solutions. Our formulation incorporates strongly resonant equations.
6
Content available Existence result for hemivariational inequality involving p(x)-Laplacian
Barnaś S.
Opuscula Mathematica
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2012
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Vol. 32, no. 3
439-454
EN
In this paper we study the nonlinear elliptic problem with p(x)-Laplacian (hemivariational inequality). We prove the existence of a nontrivial solution. Our approach is based on critical point theory for locally Lipschitz functionals due to Chang [J. Math. Anal. Appl. 80 (1981), 102-129].
7
Content available Critical points for vector-valued functions
Lucchetti R., Revalski J., Thera M.
Control and Cybernetics
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2002
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Vol. 31, no 3
545-555
EN
This paper contains a mountain pass theorem for continuous mappings, defined on a complete metric space and taking values in a real Banach space, ordered by a closed convex cone. We use the concept of critical point introduced by Degiovanni, Lucchetti and Ribarska, and we furnish a variant of their result, allowing for a localization both of the critical point and of the critical value.
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