On Some Existence Theorems for Semi-Linear Elliptic Equations.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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Boundary value problems for semilinear elliptic equations are considered. If the nonlinear terms do not grow too fast as a function of the gradient of the dependent variable and ordered upper and lower solutions are known, then maximal and minimal solutions can be obtained by an iteration procedure. Other results concerning the existence of additional solutions follow from topological principles.
- Theoretical Mathematics