Nonvariational elliptic systems
Copyright policy )Nonvariational elliptic systems
The authors deal with a comprehensive treatment of large classes of sublinear and superlinear elliptic systems, that is \[ \begin{cases} -\Delta u=f(u,v),\;-\Delta v=g(u,v) &\text{in }\Omega,\\ u=v=0 &\text{on }\partial\Omega, \end{cases} \] where \(\Omega\subset\mathbb R^N\), \(N\geq 3\), is a smooth bounded domain. Under some natural conditions on \(f\) and \(g\) they provide existence of positive solutions of (1). To this end, they use fixed point arguments.
superlinear, positive solution, fixed-point argument, sublinear, Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs, existence of positive solutions, Systems of elliptic equations, boundary value problems, Variational methods for elliptic systems, Nonlinear elliptic equations, sublinear and superlinear elliptic systems
superlinear, positive solution, fixed-point argument, sublinear, Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs, existence of positive solutions, Systems of elliptic equations, boundary value problems, Variational methods for elliptic systems, Nonlinear elliptic equations, sublinear and superlinear elliptic systems
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