Guide Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities

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Contents:


  1. Kundrecensioner
  2. Existence Result for Differential Inclusion with p(x)-Laplacian
  3. A system of evolutionary problems driven by a system of hemivariational inequalities

Khan, Regularization of non-coercive quasi variational inequalities, Control Cybern.

MI - Problem on satisfying inequalities

Goeleven and D. Mentagui, Well-posed hemivariational inequalities, Numer. Hu and Y. Fang, Levitin-Polyak well-posedness by perturbations of inverse variational inequalities, Optim. Huang nad X. Huang, X. Yang and D. Zhu, Levitin-Polyak well-posedness of variational inequality problems with functional constraints, J.

Bibliographic Information

Lignola and J. Morgan, Well-posedness for optimization problems with constraints defined by variational inequalities having a unique solution, J. Lin and C. Chuang, Well-posedness in the generalized sense for variational inclusion and disclusion problems and well-posedness for optimization problems with constraint, Nonlinear Anal. Liu and J.

Kundrecensioner

Zou, Strong convergence results for hemivariational inequalities, Sci. China Ser. A, 49 , Liu and D. Motreanu, A class of variational-hemivariational inequalities of elliptic type, Nonlinearity, 23 , Lucchetti and F. Patrone, A characterization of Tykhonov well-posedness for minimum problems with applications to variational inequalities, Numer. Migorski, A. Ochal and M.

Motreanu and P. Naniewicz and P. Panagiotopoulos, Nonconvex energy functions, hemivariational inequalities and substationarity principles, Acta Mech. Peng and S. Wu, The generalized Tykhonov well-posedness for system of vector quasi-equilibrium problems, Optim. Xiao and N.

Huang, Well-posedness for a class of variational-hemivariational inequalities with perturbations, J.

Existence Result for Differential Inclusion with p(x)-Laplacian

Theory Appl. Xiao, N. Huang and M. Wong, Well-posedness of hemivariational inequalities and inclusion problems, Taiwanese J. Zeng, S. Li, W. Zhang and X. Xue, Hadamard well-posedness for a set-valued optimization problem, Optim. Zolezzi, Extended well-posedness of optimization problems, J. The first is a topological minimax theorem: Theorem 2. The next lemma summarizes the properties of J : Lemma 4. We begin by giving an estimate of the integral which defines J : from the Lebourg mean value theorem [13, Theorem 1. Hence, J is well defined.

The main result Following [18], we first prove our main result in the form of an alternative: Theorem 4. The condition A1 is trivial. Thus, condition A2 is fulfilled. This concludes the proof. Moreover, assume that condition C is satisfied. Now we prove that the functional J admits a non-convex superlevel set. By reducing ourselves to considering symmetric functions, as said before, we easily overcome the problem of verifying condition E : Lemma 6. Now we define the class of functionals we will be dealing with: Definition 5. An important property of invariant functionals is expressed by the principle of symmetric crit- icality.

Then, every critical point of h XG is also a critical point of h. From our general result we deduce an analogous of Corollary 2, which assures the existence of at least three symmetric solutions: Corollary 3. Let F be as in Theorem 4 and satisfying condition C. Now we prove that I is G-invariant on X.

Then, applying Theorem 5, we deduce that the critical points of I XG are actually critical points of I. References [1] T. Bartsch, Z. Wang, Existence and multiplicity results for some superlinear elliptic problems on RN , Comm. Partial Differential Equations 20 — Chang, Variational methods for non-differentiable functionals and their applications to partial differential equations, J. Varga, An existence result for hemivariational inequalities, Electron. Differential Equations 37 1— Efimov, S. Stechkin, Approximate compactness and Chebyshev sets, Soviet Math.

Faraci, A.

A system of evolutionary problems driven by a system of hemivariational inequalities

Iannizzotto, An extension of a multiplicity theorem by Ricceri with an application to a class of quasi- linear equations, Studia Math. Gazzola, V. Kobayashi, M. Otani, The principle of symmetric criticality for non-differentiable mappings, J. Krawcewicz, W.


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Marzantowicz, Some remarks on the Lusternik—Schnirelman method for non-differentiable functionals invariant with respect to a finite group action, Rocky Mountain J. Motreanu, P. Motreanu, Cs.

Varga, A nonsmooth equivariant minimax principle, Comm. Panagiotopulos, Hemivariational Inequalities. Nonlinear Convex Anal. Ricceri, A general multiplicity theorem for certain nonlinear equations in Hilbert spaces, Proc. Notes 75 — Varga, Existence and infinitely many solutions for an abstract class of hemivariational inequalities, J. Related Papers. Multiple solutions for a homogeneous semilinear elliptic problem in double weighted Sobolev spaces.