Solvability of \(p\)-Laplace equations subject to three-point boundary value problems. (English) Zbl 1105.45008
This paper deals with the following model
\[ u_t={\partial\over\partial x}({\partial u^m\over\partial x}|{\partial u^m\over\partial x}|^{p-1}),\quad\text{where }m\geq 2,\;0.5\leq p\leq 1, \] which is reduced to the \(p\)-Laplace equation. The existence of solutions of this equation subject to the three point boundary value conditions are studied. Results at resonance and non-resonance for such boundary value problem are presented.
\[ u_t={\partial\over\partial x}({\partial u^m\over\partial x}|{\partial u^m\over\partial x}|^{p-1}),\quad\text{where }m\geq 2,\;0.5\leq p\leq 1, \] which is reduced to the \(p\)-Laplace equation. The existence of solutions of this equation subject to the three point boundary value conditions are studied. Results at resonance and non-resonance for such boundary value problem are presented.
Reviewer: Pavol Chocholatý (Bratislava)
MSC:
| 45K05 | Integro-partial differential equations |
| 35K35 | Initial-boundary value problems for higher-order parabolic equations |
| 26A33 | Fractional derivatives and integrals |
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