Sentence examples for degenerate problems from inspiring English sources
The left degenerate problems are algebraic equations.
In [3] the solutions of nonlinear and degenerate problems were investigated.
In the case of degenerate problems, the analysis becomes more complicated, and somewhat different techniques are required.
We test the method over the same set of highly degenerate problems used by the original authors of positive edge.
Extensions in various directions including degenerate problems [22] or elliptic systems of equations [23] were studied by many authors.
The construction of p-regularity [1 4] gives new possibilities for solving or describing degenerate problems (see, for instance, [5 7]).
Moreover, it is considered whether the degenerate problem is controllable if the control function acts on the degenerate boundary.
The Duffing equation is a degenerate problem since there exists (x^{ast}) such that it is a solution, but (operatorname{Im} F'(x^{ast})neq Y).
Indeed, for a simplified version, whose formulation is given by a degenerate problem on a rectangle, the existence and uniqueness of a solution under proper assumptions on the data can be proven.
This paper concerns the following degenerate problem: (mathscr{P} quad left { textstylebegin{array}{l@{quad}l} -operatorname{div}(a x,u,nabla u))+F x,u,nabla u)=f &mbox{in } Omega, u=0 &mbox{on } partialOmega, end{array}displaystyle right.
Secondly, for a simplified version of the original formulation, which leads to a degenerate problem on a rectangle, we prove the existence and uniqueness of a solution under proper assumptions on the data.
