The equivalence between the convergences of Mann and Ishikawa iteration methods with errors for demicontinuous -strongly accretive operators in uniformly smooth Banach spaces.
The equivalence between the Mann and Ishikawa iterations dealing with generalized contractions.
The equivalence between the -stabilities of Picard–Banach and Mann–Ishikawa iterations.
The equivalence of Mann iteration and Ishikawa iteration for -uniformly pseudocontractive or -uniformly accretive maps.
The equivalence of Mann iteration and Ishikawa iteration for non-Lipschitzian operators.
The Euler-Lagrange inclusion in Orlicz-Sobolev spaces
We establish the Euler-Lagrange inclusion of a nonsmooth integral functional defined on Orlicz-Sobolev spaces. This result is achieved through variational techniques in nonsmooth analysis and an integral representation formula for the Clarke generalized gradient of locally Lipschitz integral functionals defined on Orlicz spaces.
The existence and uniqueness of solution of Duffing equations with non- perturbation functional at nonresonance.
The existence of bounded solutions for differential equations in Hilbert spaces
The existence of bounded solutions for equations x' = A(t)x + r(x,t) is proved, where the linear part is exponentially dichotomic and the nonlinear term r satisfies some weak conditions.
The existence of positive solution to some asymptotically linear elliptic equations in exterior domains.
In this paper, we are concerned with the asymptotically linear elliptic problem -Δu + λ0u = f(u), u ∈ H01(Ω) in an exterior domain Ω = RnO (N ≥ 3) with O a smooth bounded and star-shaped open set, and limt→+∞ f(t)/t = l, 0 < l < +∞. Using a precise deformation lemma and algebraic topology argument, we prove under our assumptions that the problem possesses at least one positive solution.
The general hybrid approximation methods for nonexpansive mappings in Banach spaces.
The Idzik type quasivariational inequalities and noncompact optimization problems
The interaction of linear boundary value and nonlinear functional conditions
The existence of solutions is studied for certain nonlinear differential equations with both linear and nonlinear conditions
The iterative method of generalized -concave operators.
The Lagrange multipliers theorem for locally convex metric spaces
The large deformation of nonlinearly elastic shells in axisymmetric flows
The Newton-kantorovich Method under Mild Differentiability Conditions and the Patak Error Estimates.
The nonzero solutions and multiple solutions for a class of bilinear variational inequalities.
The -Laplace eigenvalue problem as in a Finsler metric
We consider the -Laplacian operator on a domain equipped with a Finsler metric. We recall relevant properties of its first eigenfunction for finite and investigate the limit problem as .
The -Laplacian – mascot of nonlinear analysis.
The Perturbed Generalized Tikhonov's Algorithm
We work on the research of a zero of a maximal monotone operator on a real Hilbert space. Following the recent progress made in the context of the proximal point algorithm devoted to this problem, we introduce simultaneously a variable metric and a kind of relaxation in the perturbed Tikhonov’s algorithm studied by P. Tossings. So, we are led to work in the context of the variational convergence theory.