Brezis pseudomonotone bifunctions and quasi equilibrium problems via penalization

In this paper we investigate quasi equilibrium problems in a real Banach space under the assumption of Brezis pseudomonotonicity of the function involved. To establish existence results under weak coercivity conditions we replace the quasi equilibrium problem with a sequence of penalized usual equilibrium problems. To deal with the non compact framework, we apply a regularized version of the penalty method. The particular case of set-valued quasi variational inequalities is also considered.

Existence results and two step proximal point algorithm for equilibrium problems on Hadamard manifolds

"In this paper, we study the existence of solutions of equilibrium problems in the setting of Hadamard manifolds under the pseudomonotonicity and geodesic upper sign continuity of the equilibrium bifunction and under different kinds of coercivity conditions. We also study the existence of solutions of the equilibrium problems under properly quasimonotonicity of the equilibrium bifunction. We propose a two-step proximal point algorithm for solving equilibrium problems in the setting of Hadamard manifolds. The convergence of the proposed algorithm is studied under the strong pseudomonotonicity and Lipschitz-type condition. The results of this paper either extend or generalize several known results in the literature."

A singular periodic Ambrosetti–Prodi problem of Rayleigh equations without coercivity conditions

In this paper, we use the Leray–Schauder degree theory to study the following singular periodic problems: [Formula: see text], [Formula: see text], where [Formula: see text] is a continuous function with [Formula: see text], function [Formula: see text] is continuous with an attractive singularity at the origin, and [Formula: see text] is a constant. We consider the case where the friction term [Formula: see text] satisfies a local superlinear growth condition but not necessarily of the Nagumo type, and function [Formula: see text] does not need to satisfy coercivity conditions. An Ambrosetti–Prodi type result is obtained.

Solvability of Some Perturbed Generalized Variational Inequalities in Reflexive Banach Spaces

This paper aims to discuss the solvability of some perturbed generalized variational inequalities with both the mapping and the constraint set perturbed simultaneously in reflexive Banach spaces, under some coercivity conditions. In particular, a new result that the set is directional perturbed is presented. The main results generalize and extend some known results in this area.

Ambrosetti–Prodi Periodic Problem Under Local Coercivity Conditions

In this paper we focus on the periodic boundary value problem associated with the Liénard differential equation{x^{\prime\prime}+f(x)x^{\prime}+g(t,x)=s}, wheresis a real parameter,fandgare continuous functions andgisT-periodic in the variablet. The classical framework of Fabry, Mawhin and Nkashama, related to the Ambrosetti–Prodi periodic problem, is modified to include conditions without uniformity, in order to achieve the same multiplicity result under local coercivity conditions ong. Analogous results are also obtained for Neumann boundary conditions.

From nonlinear to linearized elasticity via Γ-convergence: The case of multiwell energies satisfying weak coercivity conditions

Linearized elasticity models are derived, via Γ-convergence, from suitably rescaled nonlinear energies when the corresponding energy densities have a multiwell structure and satisfy a weak coercivity condition, in the sense that the typical quadratic bound from below is replaced by a weaker p bound, 1 < p < 2, away from the wells. This study is motivated by, and our results are applied to, energies arising in the modeling of nematic elastomers.

On a Class of Variational-Hemivariational Inequalities Involving Upper Semicontinuous Set-Valued Mappings

This paper is devoted to the various coercivity conditions in order to guarantee existence of solutions and boundedness of the solution set for the variational-hemivariational inequalities involving upper semicontinuous operators. The results presented in this paper generalize and improve some known results.