Azer Sign-changing radial solutions for a semilinear problem on exterior domains with nonlinear boundary conditions

existence of sign radial solution

Resumo

In this paper we are interested to the existence and multiplicity of sign changing radial solutions of problem of elliptic equations $\Delta U(x)+\varphi(|x|)f(U)=0$ with a nonlinear boundary conditions on exterior of the unite ball centered at the origin in $\mathbb{R}^{N}$ such that $ u(x) \rightarrow 0$ as $ |x|\to \infty $, with any given number of zeros where the nonlinearity $ f(u) $ is odd, superlinear for $ u $ lager enough and $ f<0 $ on $(0,\beta)$, $ f>0$ on $(\beta,\infty) $. The function $\varphi>0$ is $ C^{1} $ on $ [R,\infty) $ where $ 0<\varphi(|x|)\leq c_0\,|x|^{-\alpha}$ with $ \alpha>2(N-1) $ and $ N>2 $ for large $ |x| $.

Downloads

Não há dados estatísticos.

Biografia do Autor

Azeroual boubker, National school of applied sciences

Departement of Mathematics and Decision Making

Abderrahim Zertiti, National School of Applied Sciences

Department of Mathematics

Referências

B. Azeroual, A. Zertiti; On multiplicity of radial solutions to Dirichlet problem involving the p-Laplacian on exterior domains, Internatinal Journal of Applied Mathematics, Vol31(2018),No. 1, pp 121-147.

H. Berestycki, P. L. Lions, and L.A. Peletier; An ODE Approach to the Existence of Positive Solutions for Semilinear Problems in RN, Ind. Univ. Math. J., 30(1) (1981), pp 141-157.

H. Berestycki, P. L. Lions; Non-linear scalar field equations II. Existence of infinitely many solutions, Arch. Rational Mech. Anal. 82(1983), pp 347-375.

A. Castro, L. Sankar and R. Shivaji; Uniqueness of nonnegative solutions for semipositone problems on exterior domains, J. Math. Anal. Appl, 394(2012), pp. 432-437.

M. Chhetri, L. Sankar and R. Shivaji; Positive solutions for a class of superlinear semipositone systems on exterior domains, Bound. Value Probl, (2014), pp. 198-207.

P. Hartman; Ordinary Differential Equation, second edition , Society for Industrial and Applied Mathematics, Philadelphia (2002).

J. Iaia; Existence and nonexistence for semilinear equations on exterior domains, Partial. Diff. Equ., Vol.30(2017), No. 4, pp 299-313.

J. Iaia; Existence of solutions for semilinear problems with prescribed number of zeros on exterior domains, Journal of Mathematical Analysis and Applications, 446(2017), 591-604.

J. Iaia; Existence of solutions for semilinear problems on exterior domains, Electronic journal of differential equations, 34(2020), 1-10.

C.K.R.T. Jones and T. Kupper; On the infinitely many solutions of a semilinear elliptic equation, SIAM J. Math. Anal. 17 (1986), pp 803-835.

J. Joshi, J. Iaia; Infinitely many solutions for a semilinear problem on exterior domains with nonlinear boundary condition, Electronic Journal of Differential Equations. vol. 2018(2018), No. 108, pp 1-10.

E. K. Lee, R. Shivaji and B. Son; Positive solutions for infinite semipositone problems on exterior domains, Differ. Integral Equ., 24(2011), 861-875.

K. Mcleod, W. C. Troy, F. B. Weissler; Radial solution of u + f(u) = 0 with prescribed numbers of zeros, Journal of Differential Equation, Volume 83,(1990), pp. 368-378.

L. Sankar, S. Sasi and R. Shivaji; Semipositone problems with falling zeros on exterior domains, J. Math. Anal. Appl., 401(2013), 146-153.

Publicado
2024-05-31
Seção
Artigos