Existence of solutions for some fourth-order nonlinear elliptic problems

Conditions for the existence of solutions of a class of elliptic problems with nonconvex constraints are given in the general framework of pseudo-monotone operators. Applications are considered in unilateral problems of free boundary type, yielding the solvability of a Reynold's lubrication model and of a biological population problem with nonlocal terms and global constraints.

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Some fourth order nonlinear elliptic problems related to epitaxial growth

Journal of Differential Equations ◽

10.1016/j.jde.2012.12.012 ◽

2013 ◽

Vol 254 (6) ◽

pp. 2515-2531 ◽

Cited By ~ 13

Author(s):

Carlos Escudero ◽

Ireneo Peral

Keyword(s):

Epitaxial Growth ◽

Fourth Order ◽

Elliptic Problems ◽

Nonlinear Elliptic Problems ◽

Nonlinear Elliptic

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Compact embeddings in the generalized Sobolev space and existence of solutions for nonlinear elliptic problems

Nonlinear Analysis ◽

10.1016/j.na.2008.12.046 ◽

2009 ◽

Vol 71 (5-6) ◽

pp. 1534-1541 ◽

Cited By ~ 6

Author(s):

Takao Ohno

Keyword(s):

Sobolev Space ◽

Existence Of Solutions ◽

Elliptic Problems ◽

Nonlinear Elliptic Problems ◽

Nonlinear Elliptic ◽

Compact Embeddings

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Compact embeddings for Sobolev spaces of variable exponents and existence of solutions for nonlinear elliptic problems involving the p(x)-Laplacian and its critical exponent

Annales Academiae Scientiarum Fennicae Mathematica ◽

10.5186/aasfm.2010.3507 ◽

2010 ◽

Vol 35 ◽

pp. 115-130 ◽

Cited By ~ 16

Author(s):

Yoshihiro Mizuta ◽

Takao Ohno ◽

Tetsu Shimomura ◽

Naoki Shioji

Keyword(s):

Critical Exponent ◽

Sobolev Spaces ◽

Existence Of Solutions ◽

Elliptic Problems ◽

Variable Exponents ◽

Nonlinear Elliptic Problems ◽

Nonlinear Elliptic ◽

Compact Embeddings

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Sign-changing solutions for some fourth-order nonlinear elliptic problems

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2007.12.020 ◽

2008 ◽

Vol 342 (1) ◽

pp. 542-558 ◽

Cited By ~ 30

Author(s):

Jianwen Zhou ◽

Xian Wu

Keyword(s):

Fourth Order ◽

Elliptic Problems ◽

Nonlinear Elliptic Problems ◽

Nonlinear Elliptic ◽

Sign Changing Solutions

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Existence results for some fourth-order nonlinear elliptic problems

Nonlinear Analysis ◽

10.1016/s0362-546x(99)00328-4 ◽

2001 ◽

Vol 45 (1) ◽

pp. 29-36 ◽

Cited By ~ 24

Author(s):

Zhang Jihui

Keyword(s):

Fourth Order ◽

Elliptic Problems ◽

Existence Results ◽

Nonlinear Elliptic Problems ◽

Nonlinear Elliptic

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Existence results for some fourth-order nonlinear elliptic problems of local superlinearity and sublinearity

Journal of Mathematical Analysis and Applications ◽

10.1016/s0022-247x(03)00170-7 ◽

2003 ◽

Vol 281 (2) ◽

pp. 633-640 ◽

Cited By ~ 29

Author(s):

Guixiang Xu ◽

Jihui Zhang

Keyword(s):

Fourth Order ◽

Elliptic Problems ◽

Existence Results ◽

Nonlinear Elliptic Problems ◽

Nonlinear Elliptic

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On a subharmonic functional in fourth order nonlinear elliptic problems

Journal of Mathematical Analysis and Applications ◽

10.1016/0022-247x(81)90243-2 ◽

1981 ◽

Vol 83 (1) ◽

pp. 20-25 ◽

Cited By ~ 7

Author(s):

Vinod B Goyal ◽

Philip W Schaefer

Keyword(s):

Fourth Order ◽

Elliptic Problems ◽

Nonlinear Elliptic Problems ◽

Nonlinear Elliptic

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Applications of Riccati-type inequalities to asymptotic theory of elliptic problems

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210507000959 ◽

2009 ◽

Vol 139 (5) ◽

pp. 1071-1089

Author(s):

Hiroyuki Usami

Keyword(s):

Asymptotic Behaviour ◽

Asymptotic Theory ◽

Existence Of Solutions ◽

Necessary Conditions ◽

Elliptic Problems ◽

Nonlinear Elliptic Problems ◽

Liouville Type ◽

One Dimensional ◽

Nonlinear Elliptic ◽

Liouville Type Theorems

We show how one-dimensional generalized Riccati-type inequalities can be employed to analyse asymptotic behaviour of solutions of elliptic problems. We give Liouville-type theorems as well as necessary conditions for the existence of solutions of specified asymptotic behaviour of nonlinear elliptic problems.

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