1,721,041 research outputs found
Fourth-order nonlinear Schrödinger equations in an exterior domain
No full textWe discuss necessary conditions on the power p>1 for the existence of weak solutions to the fourth-order nonlinear Schrödinger equation (Formula presented.). The equation is studied in an exterior domain (Formula presented.), where (Formula presented.) and (Formula presented.) is the unit closed ball. We show that no weak solution may exist for critical and subcritical powers p. In the first scenario, the critical power depends on an integral sign condition on the boundary conditions (Formula presented.) or (Formula presented.), for (Formula presented.). Moreover, the critical power is sharp, in the sense that (stationary) solutions may be constructed for suitable data for any supercritical power. In the second scenario, the critical power depends on an integral sign condition on the initial value (Formula presented.) but it becomes larger if a stronger sign condition on h is assumed as (Formula presented.)
A Note on Recent Fixed Point Results Involving <i>g</I>-quasicontractive Type Mappings in Partially Ordered Metric Spaces
No full textKARAPINAR, ERDAL/0000-0002-6798-3254; Samet, Bessem/0000-0002-6769-3417In this note, we establish the equivalence between recent fixed point theorems involving quasicontractive type mappings in metric spaces endowed with a partial order.Visiting Professor Programming at King Saud UniversityThe authors thank the Visiting Professor Programming at King Saud University for funding this work. The authors thank the anonymous referees for their remarkable comments, suggestions and ideas that helped to improve this paper
The Role of Convection in the Limit Shape of the Critical Front Profile for Born-Infeld Diffusion Models
No full textIn this paper, we deal with models with Born-Infeld (or relativistic) type diffusion and monostable reaction, investigating the effect of the introduction of a convection term on the limit shape of the critical front profile for vanishing diffusion. We first provide an estimate of the critical speed and then, through a careful analysis of an equivalent first-order problem, we show that different convection terms may lead either to a complete sharpening of the limit profile or to its complete regularization, presenting some related numerical simulations
Fixed Point Theorems for Various Classes of Cyclic Mappings
No full textAydi, Hassen/0000-0003-4606-7211; KARAPINAR, ERDAL/0000-0002-6798-3254; Samet, Bessem/0000-0002-6769-3417; , Hassen/0000-0003-3896-3809We introduce new classes of cyclic mappings and we study the existence and uniqueness of fixed points for such mappings. The presented theorems generalize and improve several existing results in the literature
Pseudo Picard Operators On Generalized Metric Spaces
No full textAltun, Ishak/0000-0002-7967-0554; Samet, Bessem/0000-0002-6769-3417In this paper, we present a new class of pseudo Picard operators in the setting of generalized metric spaces introduced recently in [M. JLELI AND B. SAMET: A generalized metric space and related fixed point theorems, Fixed Point Theory Appl., (2015) 2015:61]. An example is provided to illustrate the main result.Deanship of Scientific Research at King Saud UniversityDeanship of Scientific Research at King Saud University [RGP-237]The second author extends his appreciation to the Deanship of Scientific Research at King Saud University for funding this work through research group No RGP-237
Fixed Point Results for Α-ψ<sub>λ</Sub>-contractions on Gauge Spaces and Applications
No full textKARAPINAR, ERDAL/0000-0002-6798-3254; Jleli, Mohamed/0000-0002-6095-5875; Samet, Bessem/0000-0002-6769-3417We extend the concept of alpha-psi-contractive mappings introduced recently by Samet et al. (2012) to the setting of gauge spaces. New fixed point results are established on such spaces, and some applications to nonlinear integral equations on the half-line are presented.Research Center, College of Science, King Saud UniversityThis work is supported by the Research Center, College of Science, King Saud University
A Short Note on the Equivalence Between 'best Proximity' Points and 'fixed Point' Results
No full textJleli, Mohamed/0000-0002-6095-5875; KARAPINAR, ERDAL/0000-0002-6798-3254; Samet, Bessem/0000-0002-6769-3417In this short note, we notice that, unexpectedly, some existing fixed point results and recently announced best proximity point results are equivalent.Visiting Professor Programming at King Saud UniversityThe authors thank the Visiting Professor Programming at King Saud University for funding this work. The authors thank to anonymous referees for their remarkable comments, suggestion and ideas that helps to improve this paper
On Cyclic (ψ, Φ)-Contractions in Kaleva-seikkala's Type Fuzzy Metric Spaces
No full textJleli, Mohamed/0000-0002-6095-5875; KARAPINAR, ERDAL/0000-0002-6798-3254; Samet, Bessem/0000-0002-6769-3417In this paper we introduce the notion of cyclic (psi, phi)-contractions on fuzzy metric spaces in the sense of Kaleva and Seikkala, and we discuss the existence and uniqueness of fixed points for mappings satisfying such type of contractions.King Saud University, Deanship of Scientific Research, College of Science Research CenterThis project was supported by King Saud University, Deanship of Scientific Research, College of Science Research Center
A new detailed explanation of the Tacoma collapse and some optimization problems to improve the stability of suspension bridges
Full text linkWe give a new full explanation of the Tacoma Narrows Bridge collapse, occurred on November 7, 1940. Our explanation involves both structural phenomena, such as parametric resonances, and sophisticated mathematical tools, such as the Floquet theory. Contrary to all previous attempts, our explanation perfectly fits, both qualitatively and quantitatively, with what was observed that day. With this explanation at hand, we set up and partially solve some optimal control and shape optimization problems (both analytically and numerically) aiming to improve the stability of bridges. The control parameter to be optimized is the strength of a partial damping term whose role is to decrease the energy within the deck. Shape optimization intends to give suggestions for the design of future bridges
Fixed Point Results for Almost Generalized Cyclic (ψ, Φ)-Weak Contractive Type Mappings With Applications
No full textKARAPINAR, ERDAL/0000-0002-6798-3254; Jleli, Mohamed/0000-0002-6095-5875; Samet, Bessem/0000-0002-6769-3417We define a class of almost generalized cyclic (psi,phi)-weak contractive mappings and discuss the existence and uniqueness of fixed points for such mappings. We present some examples to illustrate our results. Moreover, we state some applications of our main results in nonlinear integral equations.Research Center, College of Science, King Saud UniversityM. Jleli and B. Samet are supported by the Research Center, College of Science, King Saud University
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