By a new approach, we present a new existence result of positive solutions to the following Dirichlet boundary value problem, It is remarkable that the result of this paper is not obtained by employing the fixed-point theorems in cone and the method of the lower and upper functions. Our nonlinearit
Nonnegative solutions of singular boundary value problems with sign changing nonlinearities
✍ Scribed by R.P. Agarwal; S. Staněk
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 639 KB
- Volume
- 46
- Category
- Article
- ISSN
- 0898-1221
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
We present two new existence reeults for the initial value problem d = q(t)f(t,g), 0 < t < T, with y(O) = 0. The nonlinearity f is allowed to change sign and singularities at y = 0 and/or t = 0 are dimmed.
For the 2nth-order boundary value problem c~y (2i) (0) -fliy (2i+1) (0) = a~y (2i) (1) +/3~y (2i+1) (1) = 0, O 1, growth conditions are imposed on f which yield the existence of at least two symmetric positive solutions by using the fixed-point theorem in double cones.
By constructing available operators, some new existence theorems of positive solutions are obtained for a class of three-point boundary value problems u"+Ah(t)f(t,u)=O, 0<t<l, ~(0) -Z~'(0) = 0, u(1) = ~(~), where f is allowed to change sign, ~ C (0,1). The associated Green's function for the above p