On sign-changing solutions for nonlinear operator equations
Copyright policy )On sign-changing solutions for nonlinear operator equations
In the paper, the existence of sign-changing solutions for nonlinear operator equations in ordered Banach spaces is discussed by using the topological degree and fixed point index theory. The authors obtain some new three-solution theorems for fixed point equations of increasing operators and for general operators. The three-solution theorems are different from those of Amann and Leggett-Williams. In these theorems, all the three solutions are nonzero: one is positive, another is negative and the third one is sign-changing. These results are significant. The authors also apply their results to an integral equation and a boundary value problem for a differential equation.
- Shanxi University China (People's Republic of)
Nonlinear boundary value problems for ordinary differential equations, Degree theory for nonlinear operators, Applications of operator theory to differential and integral equations, Equations involving nonlinear operators (general), Applied Mathematics, e-Continuous, completely continuous operator, The index of isolated zero point, Completely continuous operator, cone, Fixed-point theorems, Fixed point index, Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces, 3-solution theorem, fixed point index, Cone, topological degree, Analysis
Nonlinear boundary value problems for ordinary differential equations, Degree theory for nonlinear operators, Applications of operator theory to differential and integral equations, Equations involving nonlinear operators (general), Applied Mathematics, e-Continuous, completely continuous operator, The index of isolated zero point, Completely continuous operator, cone, Fixed-point theorems, Fixed point index, Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces, 3-solution theorem, fixed point index, Cone, topological degree, Analysis
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