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Volumn 40, Issue 5, 2009, Pages 2034-2054

On a fourth order nonlinear elliptic equation with negative exponent

Author keywords

Electrostatic actuation; Fourth Order; Pull in threshold; Touch down

Indexed keywords

ASYMPTOTIC BEHAVIORS; ELECTROSTATIC ACTUATION; FOURTH ORDER; FOURTH-ORDER EQUATIONS; MAXIMAL SOLUTION; NON-LINEAR ELLIPTIC EQUATION; PHYSICAL DOMAIN; PULL-IN THRESHOLD; SMOOTH DOMAINS; THREE DIMENSIONS; TOUCH-DOWN;

EID: 70349218381     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/070703375     Document Type: Article
Times cited : (50)

References (27)
  • 1
    • 84980075953 scopus 로고
    • Estimates near the boundary for solutions of elliptic partial differential equations, satisfying general boundary conditions
    • S. Agmon, A. Douglis, and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations, satisfying general boundary conditions, I, Comm. Pure Appl. Math., 12 (1959), pp. 623-727.
    • (1959) I, Comm. Pure Appl. Math. , vol.12 , pp. 623-727
    • Agmon, S.1    Douglis, A.2    Nirenberg, L.3
  • 2
    • 0032368532 scopus 로고    scopus 로고
    • Long-wave instabilities and saturation in thin film equations
    • A. L. Bertozzi and M. C. Pugh, Long-wave instabilities and saturation in thin film equations, Comm. Pure Appl. Math., 51 (1998), pp. 625-661.
    • (1998) Comm. Pure Appl. Math. , vol.51 , pp. 625-661
    • Bertozzi, A.L.1    Pugh, M.C.2
  • 3
    • 0039623018 scopus 로고    scopus 로고
    • Finite-time blow-up of solutions of some long-wave unstable thin film equations
    • A. L. Bertozzi and M. C. Pugh, Finite-time blow-up of solutions of some long-wave unstable thin film equations, Indiana Univ. Math. J., 49 (2000), pp. 1323-1366.
    • (2000) Indiana Univ. Math. J. , vol.49 , pp. 1323-1366
    • Bertozzi, A.L.1    Pugh, M.C.2
  • 4
    • 77954784778 scopus 로고
    • u in two dimensions
    • H. Brezis and F. Merle, Uniform estimates and blow-up behavior for solutions of -λu =V(x)eu in two dimensions, Comm. Partial Differential Equations, 16 (1991), pp. 1223-1254.
    • (1991) Comm. Partial Differential Equations , vol.16 , pp. 1223-1254
    • Brezis, H.1    Merle, F.2
  • 5
    • 84972262906 scopus 로고    scopus 로고
    • Nonlinear stability of evaporating /condensing liquid films
    • J. Burelbach, S. G. Bankoff, and S. H. Davis, Nonlinear stability of evaporating /condensing liquid films, J. Fluid Mech., 195 (1998), pp. 463-494.
    • (1998) J. Fluid Mech. , vol.195 , pp. 463-494
    • Burelbach, J.1    Bankoff, S.G.2    Davis, S.H.3
  • 6
    • 0016643640 scopus 로고
    • Some continuation and variational methods for positive solutions of nonlinear elliptic eigenvalue problems
    • M. G. Crandall and P. H. Rabinowitz, Some continuation and variational methods for positive solutions of nonlinear elliptic eigenvalue problems, Arch. Ration. Mech. Anal., 58 (1975), pp. 207-218.
    • (1975) Arch. Ration. Mech. Anal. , vol.58 , pp. 207-218
    • Crandall, M.G.1    Rabinowitz, P.H.2
  • 7
    • 36248990914 scopus 로고    scopus 로고
    • Compactness along the branch of semi-stable and unstable solutions for an elliptic problem with a singular nonlinearity
    • P. Esposito, N. Ghoussoub, and Y. Guo, Compactness along the branch of semi-stable and unstable solutions for an elliptic problem with a singular nonlinearity, Comm. Pure Appl. Math., 60 (2008), pp. 1731-1768.
    • (2008) Comm. Pure Appl. Math. , vol.60 , pp. 1731-1768
    • Esposito, P.1    Ghoussoub, N.2    Guo, Y.3
  • 10
    • 34547676625 scopus 로고    scopus 로고
    • On the partial differential equations of electrostatic MEMS devices: Stationary case
    • N. Ghoussoub and Y. Guo, On the partial differential equations of electrostatic MEMS devices: Stationary case, SIAM J. Math. Anal., 38 (2007), pp. 1423-1449.
    • (2007) SIAM J. Math. Anal. , vol.38 , pp. 1423-1449
    • Ghoussoub, N.1    Guo, Y.2
  • 11
    • 44149127457 scopus 로고    scopus 로고
    • On the partial differential equations of electrostatic MEMS devices II dynamic case
    • N. Ghoussoub and Y. Guo, On the partial differential equations of electrostatic MEMS devices II: Dynamic case, NoDEA Nonlinear Differential Equations Appl., 15 (2008), pp. 115-145.
    • (2008) NoDEA Nonlinear Differential Equations Appl. , vol.15 , pp. 115-145
    • Ghoussoub, N.1    Guo, Y.2
  • 12
    • 41149100424 scopus 로고    scopus 로고
    • On the partial differential equations of electrostatic MEMS devices III refined touchdown behavior
    • Y. Guo, On the partial differential equations of electrostatic MEMS devices III: Refined touchdown behavior, J. Differential Equations, 244 (2008), pp. 2277-2309.
    • (2008) J. Differential Equations , vol.244 , pp. 2277-2309
    • Guo, Y.1
  • 13
    • 0037139633 scopus 로고    scopus 로고
    • Large and small solutions of a class of quasilinear elliptic eigenvalue problems
    • Z. M. Guo and J. R. L. Webb, Large and small solutions of a class of quasilinear elliptic eigenvalue problems, J. Differential Equations, 180 (2002), pp. 1-50.
    • (2002) J. Differential Equations , vol.180 , pp. 1-50
    • Guo, Z.M.1    Webb, J.R.L.2
  • 14
    • 33744509827 scopus 로고    scopus 로고
    • Hausdorff dimension of ruptures for solutions of a semilinear elliptic equation with singular nonlinearity
    • Z. M. Guo and J. C. Wei, Hausdorff dimension of ruptures for solutions of a semilinear elliptic equation with singular nonlinearity, Manuscripta Math., 120 (2006), pp. 193-209.
    • (2006) Manuscripta Math. , vol.120 , pp. 193-209
    • Guo, Z.M.1    Wei, J.C.2
  • 15
    • 77950689057 scopus 로고    scopus 로고
    • Symmetry of nonnegative solutions of a semilinear elliptic equation with singular nonlinearity
    • Z. M. Guo and J. C. Wei, Symmetry of nonnegative solutions of a semilinear elliptic equation with singular nonlinearity, Proc. Roy. Soc. Edinburgh Sect. A, 137 (2007), pp. 963-994.
    • (2007) Proc. Roy. Soc. Edinburgh Sect. A , vol.137 , pp. 963-994
    • Guo, Z.M.1    Wei, J.C.2
  • 16
    • 47949083734 scopus 로고    scopus 로고
    • Infinitely many turning points for an elliptic problem with a singular nonlinearity
    • Z. M. Guo and J. C. Wei, Infinitely many turning points for an elliptic problem with a singular nonlinearity, J. London Math. Soc, 78 (2008), pp. 21-35.
    • (2008) J. London Math. Soc. , vol.78 , pp. 21-35
    • Guo, Z.M.1    Wei, J.C.2
  • 17
    • 33644599759 scopus 로고    scopus 로고
    • Touchdown and pull-in voltage behavior of a MEMS device with varying dielectric properties
    • Y. Guo, Z. Pan, and M. J. Ward, Touchdown and pull-in voltage behavior of a MEMS device with varying dielectric properties, SIAM J. Appl. Math., 66 (2005), pp. 309-338.
    • (2005) SIAM J. Appl. Math. , vol.66 , pp. 309-338
    • Guo, Y.1    Pan, Z.2    Ward, M.J.3
  • 18
    • 0031171130 scopus 로고    scopus 로고
    • A nonlinear three-dimensional rupture theory of thin liquid films
    • C. C. Hwang, C. K. Lin, and W. Y. Uen, A nonlinear three-dimensional rupture theory of thin liquid films, J. Colloid Interf. Sci., 190 (1997), pp. 250-252.
    • (1997) J. Colloid Interf. Sci. , vol.190 , pp. 250-252
    • Hwang, C.C.1    Lin, C.K.2    Uen, W.Y.3
  • 19
    • 0034380061 scopus 로고    scopus 로고
    • Properties of steady states for thin film equations
    • 19] R. S. Laugesen and M. C. Pugh, Properties of steady states for thin film equations, European J. Appl. Math., 11 (2000), pp. 293-351.
    • (2000) European J. Appl. Math. , vol.11 , pp. 293-351
    • Laugesen, R.S.1    Pugh, M.C.2
  • 20
    • 0036647446 scopus 로고    scopus 로고
    • Energy levels of steady-states for thin-film-type equations
    • R. S. Laugesen and M. C. Pugh, Energy levels of steady-states for thin-film-type equations, J. Differential Equations, 182 (2002), pp. 377-415.
    • (2002) J. Differential Equations , vol.182 , pp. 377-415
    • Laugesen, R.S.1    Pugh, M.C.2
  • 21
    • 0034412533 scopus 로고    scopus 로고
    • Linear stability of steady states for thin film and cahn-hilliard type equations
    • R. S. Laugesen and M. C. Pugh, Linear stability of steady states for thin film and Cahn-Hilliard type equations, Arch. Ration. Mech. Anal., 154 (2000), pp. 3-51.
    • (2000) Arch. Ration. Mech. Anal. , vol.154 , pp. 3-51
    • Laugesen, R.S.1    Pugh, M.C.2
  • 22
    • 36348931123 scopus 로고    scopus 로고
    • Nonlinear non-local elliptic equation modelling electrostatic actuation
    • F. H. Lin and Y. S. Yang, Nonlinear non-local elliptic equation modelling electrostatic actuation, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 463 (2007), pp. 1323-1337.
    • (2007) Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. , vol.463 , pp. 1323-1337
    • Lin, F.H.1    Yang, Y.S.2
  • 23
    • 70350125531 scopus 로고    scopus 로고
    • Asymptotics of some nonlinear eigenvalue problems for a MEMS capacitor. Part I: Fold point asymptotics
    • to appear
    • A. Lindsay and M. Ward, Asymptotics of some nonlinear eigenvalue problems for a MEMS capacitor. Part I: Fold point asymptotics, Methods Anal. Appl., to appear.
    • Methods Anal. Appl.
    • Lindsay, A.1    Ward, M.2
  • 24
    • 0036302150 scopus 로고    scopus 로고
    • Mematical modeling of electrostatic MEMS with tailored dielectric properties
    • J. A. Pelesko, Mematical modeling of electrostatic MEMS with tailored dielectric properties, SIAM J. Appl. Math., 62 (2002), pp. 888-908.
    • (2002) SIAM J. Appl. Math. , vol.62 , pp. 888-908
    • Pelesko, J.A.1
  • 26
    • 0000031198 scopus 로고
    • Symmetry properties in systems of semilinear elliptic equations
    • W. C. Troy, Symmetry properties in systems of semilinear elliptic equations, J. Differential Equations, 42 (1981), pp. 400-413.
    • (1981) J. Differential Equations , vol.42 , pp. 400-413
    • Troy, W.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.