- Previous Article
- DCDS-S Home
- This Issue
-
Next Article
Nonlocal elliptic problems in infinite cylinder and applications
On nonlinear and quasiliniear elliptic functional differential equations
1. | Central Economics and Mathematical Institute, Russian Academie of Science, Nakhimovskii pr. 47, Moscow, 117418, Russian Federation |
References:
[1] |
H. Brésis, Équations et inéquations non linéaires dans les espaces vectoriels en dualitè, Ann. Inst. Fourier (Grenoble), 18 (1968), 115-175.
doi: 10.5802/aif.280. |
[2] |
F. E. Browder, Nonlinear elliptic boundary value problems and the generalized topological degree, Bull. Amer. Math. Soc., 76 (1970), 999-1005.
doi: 10.1090/S0002-9904-1970-12530-7. |
[3] |
H. Gajewski, K. Gróger and K. Zacharias, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Mathematische Lehrbücher und Monographien, II. Abteilung, Mathematische Monographien, Band 38, Akademie-Verlag, Berlin, 1974. |
[4] |
Yu. A. Dubinskii, Nonlinear elliptic and parabolic equations, J. Sov. Math., 12 (1979), 475-554.
doi: 10.1007/BF01089137. |
[5] |
P. Hartman and G. Stampacchia, On some nonlinear elliptic differential functional equations, Acta Math. 115 (1966), 271-310.
doi: 10.1007/BF02392210. |
[6] |
M. A. Krasnoselskii, Topological Methods in the Theory of Nonlinear Integral Equations, The Macmillan Co., New York, 1964. |
[7] |
G. I. Laptev, The first boundary problem for second-order quasilinear elliptic equations with double degeneration, Differential Equations, 30 (1994), 1057-1068. |
[8] |
J.-L. Lions, Quelques Methodes de Resolution de Problemes Aux Limities Non Lineaires, Dunod, Paris, 1969. |
[9] |
S. I. Pokhozhaev, Solvability of nonlinear equations with odd operators, Funkcional. Anal. i Prilo\v zen, 1 (1967), 66-73. |
[10] |
A. V. Razgulin, Rotational multi-petal waves in optical systems with 2-D feedback, Chaos in Optics. Proc. SPIE, ed. R.Roy, 2039 (1993), 342-352. |
[11] |
I. V. Skrypnik, Nonlinear elliptic and parabolic equations, J. Sov. Math., 12 (1979), 555-629. |
[12] |
A. L. Skubachevskii, The first boundary value problem for strongly elliptic differential-difference equations, J. Differential Equations, 63 (1986), 332-361.
doi: 10.1016/0022-0396(86)90060-4. |
[13] |
A. L. Skubachevskii., Elliptic Functional Differential Equations and Applications, Operator Theory: Advances and Applications, 91, Birkhäuser, Basel-Boston-Berlin, 1997. |
[14] |
A. L. Skubachevskii, Bifurcation of periodic solutions for nonlinear parabolic functional differential equations arising in optoelectronics, Nonlinear Anal., 32 (1998), 261-278.
doi: 10.1016/S0362-546X(97)00476-8. |
[15] |
O. V. Solonukha, On a class of essentially nonlinear elliptic differential-difference equations, Proc. of the Steklov Inst. of Math., 283 (2013), 226-244.
doi: 10.1134/S0081543813080154. |
[16] |
M. I. Vishik and O. A. Ladyzhenskaya, Boundary value problem for partial differential equations and certain classes of operator equations, American Mathematical Society Translations, Ser. 2, 10 (1958), 223-281. |
show all references
References:
[1] |
H. Brésis, Équations et inéquations non linéaires dans les espaces vectoriels en dualitè, Ann. Inst. Fourier (Grenoble), 18 (1968), 115-175.
doi: 10.5802/aif.280. |
[2] |
F. E. Browder, Nonlinear elliptic boundary value problems and the generalized topological degree, Bull. Amer. Math. Soc., 76 (1970), 999-1005.
doi: 10.1090/S0002-9904-1970-12530-7. |
[3] |
H. Gajewski, K. Gróger and K. Zacharias, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Mathematische Lehrbücher und Monographien, II. Abteilung, Mathematische Monographien, Band 38, Akademie-Verlag, Berlin, 1974. |
[4] |
Yu. A. Dubinskii, Nonlinear elliptic and parabolic equations, J. Sov. Math., 12 (1979), 475-554.
doi: 10.1007/BF01089137. |
[5] |
P. Hartman and G. Stampacchia, On some nonlinear elliptic differential functional equations, Acta Math. 115 (1966), 271-310.
doi: 10.1007/BF02392210. |
[6] |
M. A. Krasnoselskii, Topological Methods in the Theory of Nonlinear Integral Equations, The Macmillan Co., New York, 1964. |
[7] |
G. I. Laptev, The first boundary problem for second-order quasilinear elliptic equations with double degeneration, Differential Equations, 30 (1994), 1057-1068. |
[8] |
J.-L. Lions, Quelques Methodes de Resolution de Problemes Aux Limities Non Lineaires, Dunod, Paris, 1969. |
[9] |
S. I. Pokhozhaev, Solvability of nonlinear equations with odd operators, Funkcional. Anal. i Prilo\v zen, 1 (1967), 66-73. |
[10] |
A. V. Razgulin, Rotational multi-petal waves in optical systems with 2-D feedback, Chaos in Optics. Proc. SPIE, ed. R.Roy, 2039 (1993), 342-352. |
[11] |
I. V. Skrypnik, Nonlinear elliptic and parabolic equations, J. Sov. Math., 12 (1979), 555-629. |
[12] |
A. L. Skubachevskii, The first boundary value problem for strongly elliptic differential-difference equations, J. Differential Equations, 63 (1986), 332-361.
doi: 10.1016/0022-0396(86)90060-4. |
[13] |
A. L. Skubachevskii., Elliptic Functional Differential Equations and Applications, Operator Theory: Advances and Applications, 91, Birkhäuser, Basel-Boston-Berlin, 1997. |
[14] |
A. L. Skubachevskii, Bifurcation of periodic solutions for nonlinear parabolic functional differential equations arising in optoelectronics, Nonlinear Anal., 32 (1998), 261-278.
doi: 10.1016/S0362-546X(97)00476-8. |
[15] |
O. V. Solonukha, On a class of essentially nonlinear elliptic differential-difference equations, Proc. of the Steklov Inst. of Math., 283 (2013), 226-244.
doi: 10.1134/S0081543813080154. |
[16] |
M. I. Vishik and O. A. Ladyzhenskaya, Boundary value problem for partial differential equations and certain classes of operator equations, American Mathematical Society Translations, Ser. 2, 10 (1958), 223-281. |
[1] |
Mirela Kohr, Sergey E. Mikhailov, Wolfgang L. Wendland. Dirichlet and transmission problems for anisotropic stokes and Navier-Stokes systems with L∞ tensor coefficient under relaxed ellipticity condition. Discrete and Continuous Dynamical Systems, 2021, 41 (9) : 4421-4460. doi: 10.3934/dcds.2021042 |
[2] |
Chong Wang, Gang Wang, Lixia Liu. Sharp bounds on the minimum $M$-eigenvalue and strong ellipticity condition of elasticity $Z$-tensors-tensors. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021205 |
[3] |
Fabrizio Colombo, Davide Guidetti. Identification of the memory kernel in the strongly damped wave equation by a flux condition. Communications on Pure and Applied Analysis, 2009, 8 (2) : 601-620. doi: 10.3934/cpaa.2009.8.601 |
[4] |
Peter I. Kogut, Olha P. Kupenko. On optimal control problem for an ill-posed strongly nonlinear elliptic equation with $p$-Laplace operator and $L^1$-type of nonlinearity. Discrete and Continuous Dynamical Systems - B, 2019, 24 (3) : 1273-1295. doi: 10.3934/dcdsb.2019016 |
[5] |
Laura Gambera, Umberto Guarnotta. Strongly singular convective elliptic equations in $ \mathbb{R}^N $ driven by a non-homogeneous operator. Communications on Pure and Applied Analysis, , () : -. doi: 10.3934/cpaa.2022088 |
[6] |
Dorina Mitrea, Marius Mitrea, Sylvie Monniaux. The Poisson problem for the exterior derivative operator with Dirichlet boundary condition in nonsmooth domains. Communications on Pure and Applied Analysis, 2008, 7 (6) : 1295-1333. doi: 10.3934/cpaa.2008.7.1295 |
[7] |
Yoshitsugu Kabeya. Eigenvalues of the Laplace-Beltrami operator under the homogeneous Neumann condition on a large zonal domain in the unit sphere. Discrete and Continuous Dynamical Systems, 2020, 40 (6) : 3529-3559. doi: 10.3934/dcds.2020040 |
[8] |
Karim Boulabiar, Gerard Buskes and Gleb Sirotkin. A strongly diagonal power of algebraic order bounded disjointness preserving operators. Electronic Research Announcements, 2003, 9: 94-98. |
[9] |
Heinz-Jürgen Flad, Gohar Harutyunyan. Ellipticity of quantum mechanical Hamiltonians in the edge algebra. Conference Publications, 2011, 2011 (Special) : 420-429. doi: 10.3934/proc.2011.2011.420 |
[10] |
Ait Ben Hassi El Mustapha, Fadili Mohamed, Maniar Lahcen. On Algebraic condition for null controllability of some coupled degenerate systems. Mathematical Control and Related Fields, 2019, 9 (1) : 77-95. doi: 10.3934/mcrf.2019004 |
[11] |
Ryutaroh Matsumoto. Strongly secure quantum ramp secret sharing constructed from algebraic curves over finite fields. Advances in Mathematics of Communications, 2019, 13 (1) : 1-10. doi: 10.3934/amc.2019001 |
[12] |
Bernard Dacorogna. Necessary and sufficient conditions for strong ellipticity of isotropic functions in any dimension. Discrete and Continuous Dynamical Systems - B, 2001, 1 (2) : 257-263. doi: 10.3934/dcdsb.2001.1.257 |
[13] |
John Villavert. On problems with weighted elliptic operator and general growth nonlinearities. Communications on Pure and Applied Analysis, 2021, 20 (4) : 1347-1361. doi: 10.3934/cpaa.2021023 |
[14] |
Craig Cowan. Supercritical elliptic problems involving a Cordes like operator. Discrete and Continuous Dynamical Systems, 2021, 41 (9) : 4297-4318. doi: 10.3934/dcds.2021037 |
[15] |
Ole Løseth Elvetun, Bjørn Fredrik Nielsen. A regularization operator for source identification for elliptic PDEs. Inverse Problems and Imaging, 2021, 15 (4) : 599-618. doi: 10.3934/ipi.2021006 |
[16] |
Dung Le. On the regular set of BMO weak solutions to $p$-Laplacian strongly coupled nonregular elliptic systems. Discrete and Continuous Dynamical Systems - B, 2014, 19 (10) : 3245-3265. doi: 10.3934/dcdsb.2014.19.3245 |
[17] |
Xianjin Chen, Jianxin Zhou. A local min-orthogonal method for multiple solutions of strongly coupled elliptic systems. Conference Publications, 2009, 2009 (Special) : 151-160. doi: 10.3934/proc.2009.2009.151 |
[18] |
Salvatore Rionero. On the nonlinear stability of ternary porous media via only one necessary and sufficient algebraic condition. Evolution Equations and Control Theory, 2014, 3 (3) : 525-539. doi: 10.3934/eect.2014.3.525 |
[19] |
Phuong Le. Liouville theorems for stable weak solutions of elliptic problems involving Grushin operator. Communications on Pure and Applied Analysis, 2020, 19 (1) : 511-525. doi: 10.3934/cpaa.2020025 |
[20] |
Huyuan Chen, Feng Zhou. Isolated singularities for elliptic equations with hardy operator and source nonlinearity. Discrete and Continuous Dynamical Systems, 2018, 38 (6) : 2945-2964. doi: 10.3934/dcds.2018126 |
2020 Impact Factor: 2.425
Tools
Metrics
Other articles
by authors
[Back to Top]