Back
 AM  Vol.5 No.1 , January 2014
Multiple Solutions for a Class of Semilinear Elliptic Equations with Nonlinear Boundary Conditions
Abstract: In this paper, using Local Linking Theorem, we obtain the existence of multiple solutions for a class of semilinear elliptic equations with nonlinear boundary conditions, in which the nonlinearites are compared with higher Neumann eigenvalue and the first Steklov eigenvalue.
Cite this paper: Z. Yao, "Multiple Solutions for a Class of Semilinear Elliptic Equations with Nonlinear Boundary Conditions," Applied Mathematics, Vol. 5 No. 1, 2014, pp. 90-95. doi: 10.4236/am.2014.51010.
References

[1]   M. W. Steklov, “Sur les Problemes Fondamentaux de la Physique Mathematique,” Annales Scientifiques de l’école Normale Supérieure, Vol. 19, No. 1, 1902, pp. 455-490.

[2]   G. Auchmuty, “Steklov Eigenproblems and Representation of Solutions of Elliptic Boundary Value Problems,” Numerical Functional Analysis and Optimization, Vol. 25, No. 3-4, 2005, pp. 321-348. http://dx.doi.org/10.1081/NFA-120039655

[3]   H. Amann, “Nonlinear Elliptic Equations with Nonlinear Boundary Conditions,” Proceedings of the 2nd Scheveningen Conference on Differential Equations, North-Holland Mathematics Studies, Vol. 21, 1976, pp. 43-63.
http://dx.doi.org/10.1016/S0304-0208(08)71154-X

[4]   J. Mawhin and K. Schmitt, “Upper and Lower Solutions and Semilinear Second Order Elliptic Equations with Nonlinear Boundary Conditions,” Proceedings of the Royal Society of Edinburgh: Section A, Vol. 97, 1984, pp. 199-207.
http://dx.doi.org/10.1017/S030821050003198X

[5]   H. Brezis and L. Nirenberg, “Remarks on Finding Critical Points,” Communications on Pure and Applied Mathematics, Vol. 44, No. 8-9, 1991, pp. 939-963. http://dx.doi.org/10.1002/cpa.3160440808

[6]   C. V. Pao, “Nonlinear Parabolic and Elliptic Equations,” Plenum Press, New York, 1992.

[7]   N. Mavinga and M. N. Nkashama, “Steklov-Neumann Eigenproblems and Nonlinear Elliptic Equations with Nonlinear Boundary Conditions,” Journal of Differential Equations, Vol. 248, No. 5, 2010, pp. 1212-1229.
http://dx.doi.org/10.1016/j.jde.2009.10.005

 
 
Top