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Our nonlinearity may have singularity at and/or and may have singularity at.
The nonlinearity may have singularity at and/or and may have singularity at.
and obtained the existence of positive solutions by using a fixed point theorem due to Gatica et al. [14], where is decreasing in for every and may have singularity at.
Firstly, we study singular nonlinear differential equation boundary value problems, that is, (f t,x_{1},ldots,ldots,x_{n-1})) may have singularity at (t=0,1) and (x_{i}=0) ((i=1,2,ldots,n-1)), which leads to mayy difficulties in analysis.
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Under certain conditions, these conics may have singularities.
Note that the area minimizing surface (Q(Gamma )) may have singularities even if (Gamma ) is smooth.
In this paper, we construct a combined finite element and oversampling multiscale Petrov Galerkin method (FE-OMsPGM) to solve the multiscale problems which may have singularities in some special portions of the computational domain.
This upper bound for the error takes into account critical cases where the signal to be transformed may have singularities or a slow decay at infinity.
It can happen that even when the Aij are smooth functions of t or constant, the solution X may have a singularity or even infinitely many singularities.
The interesting point is that the weak singularity of restoring force (frac{alpha(t)}{x^{mu}}) at (x=0) is allowed and f may have a singularity at (x=0).
The interesting point is that the weak singularity of restoring force term (frac{alpha (t)}{x^{mu}}) at (x=0) is allowed and f may have a singularity at (x=0).
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Justyna Jupowicz-Kozak
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