Publicación: SOME RESULTS ON THE EXISTENCE AND MULTIPLICITY OF DIRICHLET TYPE SOLUTIONS FOR A SINGULAR EQUATION COMING FROM A KEPLER PROBLEM ON THE SPHERE
Fecha
2019
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NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Resumen
WE STUDY THE DIRICHLET BOUNDARY VALUE PROBLEM
U '' = H(T)/SIN(2)U, U(0+) = C(1), U(T-) = C(2),
WHERE C(1), C(2) IS AN ELEMENT OF [0,PI] AND H : [0,T] -> R IS A LEBESGUE INTEGRABLE FUNCTION. THE FORCING TERM UNDER CONSIDERATION IS THE PRODUCT OF A NONLINEARITY WHICH IS SINGULAR AT TWO POINTS WITH A WEIGHT FUNCTION H. WE PROVE THAT THE CORRESPONDING SINGULAR BOUNDARY VALUE PROBLEM IS SOLVABLE ONLY IF THE WEIGHT FUNCTION DOES NOT CHANGE ITS SIGN. THEREFORE, OUR MAIN RESULT IS STATED UNDER THIS SETTING: SUPPOSING THAT H : [0, T] [0, +INFINITY), THE EXISTENCE AND MULTIPLICITY OF SOLUTIONS TO THE AFOREMENTIONED PROBLEM IS GUARANTEED IF AND ONLY IF (H) OVER BAR IS SMALL ENOUGH.
