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Finitely many solutions for a class of boundary value problems with superlinear convex nonlinearity
Rǎdulescu, Vicenţiu, 1958-
We consider the nonlinear Sturm-Liouville problem ▫$-u'' = f(u) + h$▫ in ▫$(0,1)$▫, ▫$u(0) = u(1) = 0$▫, where ▫$h \in L^{2}(0,1)$▫ and ▫$f$▫ is a positive convex nonlinearity with superlinear growth ...at infinity. Our main result establishes that the above boundary value problem admits a finite number of solutions but it cannot have infinitely many solutions.
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