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We study the boundary value problem $- {d i v ((| \nabla u |}^{p_{1} (x) - 2} + {| \nabla u |}^{p_{2} (x) - 2}) \nabla u) = f (x, u)$ in $Ω$ , $u = 0$ on $\partial Ω$ , where $Ω$ is a smooth bounded domain in $ℝ^{N}$ . Our attention is focused on two cases when $f (x, u) = \pm (- λ | u |^{m (x) - 2} u + | u |^{q (x) - 2} u)$ , where $m (x) = max {p_{1} (x), p_{2} (x)}$ for any $x \in \bar{Ω}$ or $m (x) < q (x) < \frac{N \cdot m (x)}{(N - m (x))}$ for any $x \in \bar{Ω}$ . In the former case we show the existence of infinitely many weak solutions for any $λ > 0$ . In the latter we prove that if $λ$ is large enough then there exists a nontrivial weak solution. Our approach relies on the variable exponent theory of generalized Lebesgue-Sobolev spaces, combined with a $ℤ_{2}$ -symmetric version for even functionals...

On a hybrid method for generalized mixed equilibrium problem and fixed point problem of a family of quasi- $ϕ$ -asymptotically nonexpansive mappings in Banach spaces.

Liu, Min, Chang, Shih-Sen, Zuo, Ping (2010)

Fixed Point Theory and Applications [electronic only]

On a local degree for a class of multi-valued vector fields in infinite dimensional Banach spaces.

Benkafadar, N.M., Gel'man, B.D. (1996)

Abstract and Applied Analysis

On a new method for enlarging the radius of convergence for Newton's method

Ioannis K. Argyros (2001)

Applicationes Mathematicae

We provide new local and semilocal convergence results for Newton's method. We introduce Lipschitz-type hypotheses on the mth-Frechet derivative. This way we manage to enlarge the radius of convergence of Newton's method. Numerical examples are also provided to show that our results guarantee convergence where others do not.

On a new result on the existence of zeros due to Ricceri.

Lopes-Pinto, António J.B. (1998)

Journal of Convex Analysis

On a non linear partial differential equation having natural growth terms and unbounded solution

A. Bensoussan, L. Boccardo, F. Murat (1988)

Annales de l'I.H.P. Analyse non linéaire

On a nonlinear elliptic boundary value problem

Enayet U, Tarafdar (1982)

Commentationes Mathematicae Universitatis Carolinae

On a nonlinear elliptic system: resonance and bifurcation cases

Mario Zuluaga Uribe (1999)

Commentationes Mathematicae Universitatis Carolinae

In this paper we consider an elliptic system at resonance and bifurcation type with zero Dirichlet condition. We use a Lyapunov-Schmidt approach and we will give applications to Biharmonic Equations.

On a nonlinear integral equation with contractive perturbation.

Zhu, Huan (2011)

Advances in Difference Equations [electronic only]

On a quadratically convergent method using divided differences of order one under the gamma condition

Ioannis Argyros, Hongmin Ren (2008)

Open Mathematics

We re-examine a quadratically convergent method using divided differences of order one in order to approximate a locally unique solution of an equation in a Banach space setting [4, 5, 7]. Recently in [4, 5, 7], using Lipschitz conditions, and a Newton-Kantorovich type approach, we provided a local as well as a semilocal convergence analysis for this method which compares favorably to other methods using two function evaluations such as the Steffensen’s method [1, 3, 13]. Here, we provide an analysis...

On a secant-like method for solving generalized equations

Ioannis K. Argyros, Said Hilout (2008)

Mathematica Bohemica

In the paper by Hilout and Piétrus (2006) a semilocal convergence analysis was given for the secant-like method to solve generalized equations using Hölder-type conditions introduced by the first author (for nonlinear equations). Here, we show that this convergence analysis can be refined under weaker hypothesis, and less computational cost. Moreover finer error estimates on the distances involved and a larger radius of convergence are obtained.

On a sub-supersolution method for the prescribed mean curvature problem

Vy Khoi Le (2008)

Czechoslovak Mathematical Journal

The paper is about a sub-supersolution method for the prescribed mean curvature problem. We formulate the problem as a variational inequality and propose appropriate concepts of sub- and supersolutions for such inequality. Existence and enclosure results for solutions and extremal solutions between sub- and supersolutions are established.

On a Superlinear Elliptic Boundary Value Problem.

Peter Hess, Bernhard Ruf (1978/1979)

Mathematische Zeitschrift

On a time-dependent subdifferential evolution inclusion with a nonconvex upper-semicontinuous perturbation.

Guillaume, S., Syam, A. (2005)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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