Select Publications

Books

Goodrich C; Peterson AC, 2016, Discrete fractional calculus, http://dx.doi.org/10.1007/978-3-319-25562-0

Journal articles

Mohammed PO; Goodrich CS; Hamasalh FK; Kashuri A; Hamed YS, 2022, 'On positivity and monotonicity analysis for discrete fractional operators with discrete Mittag–Leffler kernel', Mathematical Methods in the Applied Sciences, vol. 45, pp. 6391 - 6410, http://dx.doi.org/10.1002/mma.8176

Goodrich C; Lizama C, 2022, 'Existence and monotonicity of nonlocal boundary value problems: The one-dimensional case', Proceedings of the Royal Society of Edinburgh Section A: Mathematics, vol. 152, pp. 1 - 27, http://dx.doi.org/10.1017/prm.2020.90

Goodrich CS, 2022, 'An analysis of nonlocal difference equations with finite convolution coefficients', Journal of Fixed Point Theory and Applications, vol. 24, http://dx.doi.org/10.1007/s11784-021-00914-9

Mohammed PO; Goodrich CS; Brzo AB; Baleanu D; Hamed YS, 2022, 'New classifications of monotonicity investigation for discrete operators with Mittag-Leffler kernel', Mathematical Biosciences and Engineering, vol. 19, pp. 4062 - 4074, http://dx.doi.org/10.3934/mbe.2022186

Goodrich CS, 2022, 'NONEXISTENCE AND PARAMETER RANGE ESTIMATES FOR CONVOLUTION DIFFERENTIAL EQUATIONS', Proceedings of the American Mathematical Society, Series B, vol. 9, pp. 254 - 265, http://dx.doi.org/10.1090/bproc/130

Dahal R; GOODRICH CS, 2021, 'ANALYSIS OF CONVEXITY RESULTS FOR DISCRETE FRACTIONAL NABLA OPERATORS', Rocky Mountain Journal of Mathematics, vol. 51, pp. 1981 - 2001, http://dx.doi.org/10.1216/rmj.2021.51.1981

Goodrich CS, 2021, 'A one-dimensional Kirchhoff equation with generalized convolution coefficients', Journal of Fixed Point Theory and Applications, vol. 23, http://dx.doi.org/10.1007/s11784-021-00910-z

Goodrich CS; Jonnalagadda JM, 2021, 'Monotonicity results for CFC nabla fractional differences with negative lower bound', Analysis (Germany), vol. 41, pp. 221 - 229, http://dx.doi.org/10.1515/anly-2021-0011

Goodrich CS, 2021, 'Nonlocal Differential Equations with Convolution Coefficients and Applications to Fractional Calculus', Advanced Nonlinear Studies, vol. 21, pp. 767 - 787, http://dx.doi.org/10.1515/ans-2021-2145

Goodrich CS, 2021, 'Nonlocal differential equations with concave coefficients of convolution type', Nonlinear Analysis, Theory, Methods and Applications, vol. 211, http://dx.doi.org/10.1016/j.na.2021.112437

Goodrich CS, 2021, 'Differential equations with multiple sign changing convolution coefficients', International Journal of Mathematics, vol. 32, http://dx.doi.org/10.1142/S0129167X21500579

Dahal R; Goodrich CS, 2021, 'Theoretical and numerical analysis of monotonicity results for fractional difference operators', Applied Mathematics Letters, vol. 117, http://dx.doi.org/10.1016/j.aml.2021.107104

Goodrich CS, 2021, 'Partial regularity of minimizers of asymptotically convex functionals with Morrey coefficients', Journal of Mathematical Analysis and Applications, vol. 498, http://dx.doi.org/10.1016/j.jmaa.2021.124962

Goodrich CS; Jonnalagadda JM; Lyons B, 2021, 'Convexity, monotonicity, and positivity results for sequential fractional nabla difference operators with discrete exponential kernels', Mathematical Methods in the Applied Sciences, vol. 44, pp. 7099 - 7120, http://dx.doi.org/10.1002/mma.7247

Goodrich C, 2021, 'A topological approach to a class of one-dimensional Kirchhoff equations', Proceedings of the American Mathematical Society, Series B, vol. 8, pp. 158 - 172, http://dx.doi.org/10.1090/bproc/84

Goodrich CS, 2021, 'Topological analysis of doubly nonlocal boundary value problems', Journal of Fixed Point Theory and Applications, vol. 23, http://dx.doi.org/10.1007/s11784-021-00865-1

Goodrich CS, 2021, 'A topological approach to nonlocal elliptic partial differential equations on an annulus', Mathematische Nachrichten, vol. 294, pp. 286 - 309, http://dx.doi.org/10.1002/mana.201900204

Goodrich CS; Jonnalagadda JM, 2021, 'An analysis of polynomial sequences and their application to discrete fractional operators', Journal of Difference Equations and Applications, vol. 27, pp. 1081 - 1102, http://dx.doi.org/10.1080/10236198.2021.1965132

Goodrich CS; Lyons B; Scapellato A; Velcsov MT, 2021, 'Analytical and numerical convexity results for discrete fractional sequential differences with negative lower bound', Journal of Difference Equations and Applications, vol. 27, pp. 317 - 341, http://dx.doi.org/10.1080/10236198.2021.1894142

Goodrich CS; Lyons B; Velcsov MT, 2021, 'ANALYTICAL and NUMERICAL MONOTONICITY RESULTS for DISCRETE FRACTIONAL SEQUENTIAL DIFFERENCES with NEGATIVE LOWER BOUND', Communications on Pure and Applied Analysis, vol. 20, pp. 339 - 358, http://dx.doi.org/10.3934/cpaa.2020269

Goodrich CS, 2021, 'Discrete Kirchhoff equations with sign-changing coefficients', Journal of Difference Equations and Applications, vol. 27, pp. 664 - 685, http://dx.doi.org/10.1080/10236198.2021.1929945

Dahal R; Goodrich CS; Lyons B, 2021, 'Monotonicity results for sequential fractional differences of mixed orders with negative lower bound', Journal of Difference Equations and Applications, vol. 27, pp. 1574 - 1593, http://dx.doi.org/10.1080/10236198.2021.1999434

Goodrich C; Scilla G; Stroffolini B, 2021, 'Partial regularity for minimizers of discontinuous quasiconvex integrals with general growth', Proceedings of the Royal Society of Edinburgh Section A: Mathematics, http://dx.doi.org/10.1017/prm.2021.53

Goodrich CS; Lyons B, 2020, 'Nonlocal difference equations with sign-changing coefficients', Applied Mathematics Letters, vol. 106, http://dx.doi.org/10.1016/j.aml.2020.106371

Goodrich C; Lizama C, 2020, 'Positivity, monotonicity, and convexity for convolution operators', Discrete and Continuous Dynamical Systems- Series A, vol. 40, pp. 4961 - 4983, http://dx.doi.org/10.3934/dcds.2020207

Goodrich CS; Lyons B, 2020, 'Positivity and monotonicity results for triple sequential fractional differences via convolution', Analysis (Germany), vol. 40, pp. 89 - 103, http://dx.doi.org/10.1515/anly-2019-0050

Goodrich CS; Ragusa MA; Scapellato A, 2020, 'Partial regularity of solutions to p(x)-Laplacian PDEs with discontinuous coefficients', Journal of Differential Equations, vol. 268, pp. 5440 - 5468, http://dx.doi.org/10.1016/j.jde.2019.11.026

Goodrich C; Lizama C, 2020, 'A transference principle for nonlocal operators using a convolutional approach: fractional monotonicity and convexity', Israel Journal of Mathematics, vol. 236, pp. 533 - 589, http://dx.doi.org/10.1007/s11856-020-1991-2

Goodrich CS, 2020, 'Pointwise conditions for perturbed Hammerstein integral equations with monotone nonlinear, nonlocal elements', Banach Journal of Mathematical Analysis, vol. 14, pp. 290 - 312, http://dx.doi.org/10.1007/s43037-019-00017-1

Goodrich CS; Muellner M, 2019, 'An analysis of the sharpness of monotonicity results via homotopy for sequential fractional operators', Applied Mathematics Letters, vol. 98, pp. 446 - 452, http://dx.doi.org/10.1016/j.aml.2019.07.003

Goodrich CS, 2019, 'Coercive functionals and their relationship to multiplicity of solution to nonlocal boundary value problems', Topological Methods in Nonlinear Analysis, vol. 54, pp. 409 - 426, http://dx.doi.org/10.12775/TMNA.2019.029

Goodrich CS; Ragusa MA, 2019, 'Hölder continuity of weak solutions of p-Laplacian PDEs with VMO coefficients', Nonlinear Analysis, Theory, Methods and Applications, vol. 185, pp. 336 - 355, http://dx.doi.org/10.1016/j.na.2019.03.015

Xu J; Goodrich CS; Cui Y, 2019, 'Positive solutions for a system of first-order discrete fractional boundary value problems with semipositone nonlinearities', Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, vol. 113, pp. 1343 - 1358, http://dx.doi.org/10.1007/s13398-018-0551-7

Dahal R; Goodrich CS, 2019, 'A uniformly sharp convexity result for discrete fractional sequential differences', Rocky Mountain Journal of Mathematics, vol. 49, pp. 2571 - 2586, http://dx.doi.org/10.1216/RMJ-2019-49-8-2571

Dahal R; Goodrich CS, 2019, 'An application of a nonstandard cone to discrete boundary value problems with unbounded indefinite forcing', Journal of Difference Equations and Applications, http://dx.doi.org/10.1080/10236198.2019.1639684

Dahal R; Goodrich CS, 2019, 'Mixed order monotonicity results for sequential fractional nabla differences', Journal of Difference Equations and Applications, vol. 25, pp. 837 - 854, http://dx.doi.org/10.1080/10236198.2018.1561883

Anceschi F; Goodrich CS; Scapellato A, 2019, 'Operators with gaussian kernel bounds on mixed morrey spaces', Filomat, vol. 33, pp. 5219 - 5230, http://dx.doi.org/10.2298/FIL1916219A

Goodrich CS, 2019, 'Sharp monotonicity results for fractional nabla sequential differences', Journal of Difference Equations and Applications, vol. 25, pp. 801 - 814, http://dx.doi.org/10.1080/10236198.2018.1542431

Goodrich CS, 2018, 'A general low-order partial regularity theory for asymptotically convex functionals with asymptotic dependence on the minimizer', Calculus of Variations and Partial Differential Equations, vol. 57, http://dx.doi.org/10.1007/s00526-018-1422-y

Goodrich CS, 2018, 'Partial regularity of minimizers of functionals with discontinuous coefficients of low integrability with applications to nonlinear elliptic systems', Communications in Partial Differential Equations, vol. 43, pp. 1599 - 1626, http://dx.doi.org/10.1080/03605302.2018.1517794

Goodrich CS, 2018, 'Radially symmetric solutions of elliptic PDEs with uniformly negative weight', Annali di Matematica Pura ed Applicata, vol. 197, pp. 1585 - 1611, http://dx.doi.org/10.1007/s10231-018-0738-8

Goodrich CS, 2018, 'Monotonicity and non-monotonicity results for sequential fractional delta differences of mixed order', Positivity, vol. 22, pp. 551 - 573, http://dx.doi.org/10.1007/s11117-017-0527-4

Goodrich CS, 2018, 'Perturbed Integral Operator Equations of Volterra Type with Applications to p -Laplacian Equations', Mediterranean Journal of Mathematics, vol. 15, http://dx.doi.org/10.1007/s00009-018-1090-3

Goodrich CS, 2018, 'A uniformly sharp monotonicity result for discrete fractional sequential differences', Archiv der Mathematik, vol. 110, pp. 145 - 154, http://dx.doi.org/10.1007/s00013-017-1106-4

Goodrich CS, 2018, 'New Harnack inequalities and existence theorems for radially symmetric solutions of elliptic PDEs with sign changing or vanishing Green's function', Journal of Differential Equations, vol. 264, pp. 236 - 262, http://dx.doi.org/10.1016/j.jde.2017.09.011

Goodrich CS, 2017, 'The effect of a nonstandard cone on existence theorem applicability in nonlocal boundary value problems', Journal of Fixed Point Theory and Applications, vol. 19, pp. 2629 - 2646, http://dx.doi.org/10.1007/s11784-017-0448-7

Goodrich CS, 2017, 'Partial Lipschitz regularity of minimizers of asymptotically convex functionals with general growth conditions', Journal of Differential Equations, vol. 263, pp. 4400 - 4428, http://dx.doi.org/10.1016/j.jde.2017.05.017

Goodrich CS, 2017, 'A new coercivity condition applied to semipositone integral equations with nonpositive, unbounded nonlinearities and applications to nonlocal BVPs', Journal of Fixed Point Theory and Applications, vol. 19, pp. 1905 - 1938, http://dx.doi.org/10.1007/s11784-016-0340-x

Erbe L; Goodrich CS; Jia B; Peterson A, 2017, 'Monotonicity results for delta fractional differences revisited', Mathematica Slovaca, vol. 67, pp. 895 - 906, http://dx.doi.org/10.1515/ms-2017-0018


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