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Chang-Jun Li and Xiang Gao

Abstract

In this paper, we present a new proof of the upper and lower bound estimates for the first Dirichlet eigenvalue λ1D(B(p,r)) of Laplacian operator for the manifold with Ricci curvature Rc−K, by using Li-Yau’s gradient estimate for the heat equation.

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Mohsen Khaleghi Moghadam and Renata Wieteska

, Existence results to a nonlinear p ( k )- Laplacian difference equation, J. Difference Equ. Appl. Vol. 23, No. 10 (2017), 1652–1669 [26] M. Khaleghi Moghadam and J. Henderson, Triple solutions for a dirichlet boundary value problem involving a perturbed discrete p ( k ) -laplacian operator, Open Math., 15 (2017) 1075–1089. [27] M. Khaleghi Moghadam, S. Heidarkhani and J. Henderson, Infinitely many solutions for perturbed difference equations, J. Difference Equ. Appl. 207 (2014), 1055–1068. [28] M. Khaleghi Moghadam, L. Li and S. Tersian

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Abdelouahed El Khalil

. 349 (1997), 171-188. [20] Edmunds, D.E., Evans, W.D., Spectral Theory and Differential Operators , Clarendon Press, University Oxford Press, New York, 1987. [21] El khalil, A., Touzani A.: On the first eigencurve of the p-Laplacian, Partial Differential Equations, Lecture Notes in Pure and Applied Mathematics Series, Marcel Dekker, Inc. 229 (2002), 195-205. [22] Gilbarg, D., Trudinger, N.: Elliptic Partial Differential Equations of Second order , Springer, Berlin, 1983. [23] Lindqvist, P.: On the equation div(|∇ u | p −2 ∇ u ) + λ | u

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Waldo Arriagada and Jorge Huentutripay

References [1] R.A. Adams and J.F. Fournier, Sobolev Spaces, 2nd edition, Academic Press, 2003. [2] W. Arriagada and J. Huentutripay. A Harnack's inequality in Orlicz- Sobolev spaces, to appear in Studia Mathematica, (2017) [3] W. Arriagada and J. Huentutripay. Blow-up rates of large solutions for a φ-Laplacian problem with gradient term, Proc. A Royal Soc. Edinburgh, 144, No. 1, (2014) 669-689. [4] W. Arriagada and J. Huentutripay. Characterization of a homoge- neous Orlicz space, Electron. J

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M.S. Shahrokhi-Dehkordi

, S. A. Marano, K. Perera: On a class of critical (p; q)-Laplacian problems. Nonlinear Di_er. Equ. Appl. 22 (2015) 1959{1972. [5] L. Cherfils, Y. Iåyasov: On the stationary solutions of generalized reaction di_usion equations with p&q-Laplacian. Commun. Pure Appl. Anal. 4 (1) (2005) 9{22. [6] G. H. Derrick: Comments on nonlinear wave equations as models for elementary particles. J. Math. Phys. 5 (1964) 1252{1254. [7] P. C. Fife: Mathematical aspects of reacting and di_using systems. Springer, Berlin (1979

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Konan Charles Etienne Goli and Assohoun Adjé

: Nonhomogeneous boundary value problems for some nonlinear equations with singular ∅-Laplacian. J. Math. Anal. Appl. 352 (2009) 218-233. [4] P.G. Bergmann: Introduction to the Theory of Relativity. Dover Publications, New York (1976). [5] H. Brezis, J. Mawhin: Periodic solutions of the forced relativistic pendulum. Differential Integral Equations 23 (2010) 801-810. [6] D. Franco, D. O'Regan: Existence of solutions to second order problems with nonlinear boundary conditions. In: Proceedings of the Fourth International Conference on

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Vagif S. Guliyev and Yagub Y. Mammadov

, Boundedness of the maximal, potential and singular operators in the generalized Morrey spaces, J. Inequal. Appl., 2009, Art. ID 503948, 20 pp. [16] S. Giulini, Approximation and Besov spaces on stratified groups. Proc. Amer. Math. Soc. 96 (1986), No. 4, 569-578. [17] D.S Jerison, The Dirichlet problem for the Kohn Laplacian on the Heisenberg group. I., J. Funct. Anal., 43 (1981), 97142. [18] D.S Jerison, The Dirichlet problem for the Kohn Laplacian on the Heisenberg group. II., J. Funct. Anal., 43 (1981), 224257

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Vladimir B. Vasilyev

the theory of boundary value problems in non-smooth domains. Kluwer Acad. Publ., Dordrecht, 2000. [5] SOLONNIKOV, V. A.-FROLOVA, E. V.: On the third value problem for the Laplace equation in a plane sector and application to parabolic problems , Algebra Anal. 2 (1990), 213-241. [6] BAZALIY, B. V.-VASYLYEVA, N.: On the solvability of a transmission problem for the Laplace operator with a dynamic boundary condition on a nonregular interface, J. Math. Anal. Appl. 393 (2012), 651-670. [7] VASILYEV, V. B.: Discrete

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Geeta Hanji and M. Latte

A new impulse noise detection and filtering algorithm

A new impulse detection and filtering algorithm is proposed for restoration of images that are highly corrupted by impulse noise. It is based on the average absolute value of four convolutions obtained by one-dimensional Laplacian operators. The proposed algorithm can effectively remove the impulse noise with a wide range of noise density and produce better results in terms of the qualitative and quantitative measures of the images even at noise density as high as 90%. Extensive simulations show that the proposed algorithm provides better performance than many of the existing switching median filters in terms of noise suppression and detail preservation.