Geodesic
On some boundary value problems for second order nonlinear differential equations
Mathematica Bohemica, Tome 137 (2012) no. 2, pp. 113-122.

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We investigate two boundary value problems for the second order differential equation with $p$-Laplacian \[ (a(t)\Phi _{p}(x'))'=b(t)F(x), \quad t\in I=[0,\infty ), \] where $a$, $b$ are continuous positive functions on $I$. We give necessary and sufficient conditions which guarantee the existence of a unique (or at least one) positive solution, satisfying one of the following two boundary conditions: \[ {\rm i)}\ x(0)=c>0, \ \lim _{t\rightarrow \infty }x(t)=0; \quad {\rm ii)}\ x'(0)=d0, \ \lim _{t\rightarrow \infty }x(t)=0. \]
DOI : 10.21136/MB.2012.142856
Classification : 34B18, 34B40, 34C10, 34D05
Keywords: boundary value problem; $p$-Laplacian; half-linear equation; positive solution; uniqueness; decaying solution; principal solution 
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     title = {On some boundary value problems for second order nonlinear differential equations},
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Došlá, Zuzana; Marini, Mauro; Matucci, Serena. On some boundary value problems for second order nonlinear differential equations. Mathematica Bohemica, Tome 137 (2012) no. 2, pp. 113-122. doi : 10.21136/MB.2012.142856. http://geodesic.mathdoc.fr/articles/10.21136/MB.2012.142856/

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