Positive solutions for some quasilinear elliptic equations with natural growths
We shall prove an existence result for a class of quasilinear elliptic equations with natural growth. The model problem is
We shall prove an existence result for a class of quasilinear elliptic equations with natural growth. The model problem is
The existence of a positive radial solution for a sublinear elliptic boundary value problem in an exterior domain is proved, by the use of a cone compression fixed point theorem. The existence of a nonradial, positive solution for the corresponding nonradial problem is obtained by the sub- and supersolution method, under an additional monotonicity assumption.
We consider the existence of positive solutions of -pu=g(x)|u|p-2u+h(x)|u|q-2u+f(x)|u|p*-2u(1) in , where , , , the critical Sobolev exponent, and , . Let be the principal eigenvalue of -pu=g(x)|u|p-2u in , g(x)|u|p>0, (2) with the associated eigenfunction. We prove that, if , if and if , then there exist and , such that for and , (1) has at least one positive solution.
For semilinear elliptic equations of critical exponential growth we establish the existence of positive solutions to the Dirichlet problem on suitable non-contractible domains.
In the paper the differential inequality where , , is studied. Sufficient conditions on the function are established, which guarantee nonexistence of an eventually positive solution. The generalized Riccati transformation is the main tool.
We study the existence and nonexistence of positive solutions of nonlinear elliptic systems in an annulus with Dirichlet boundary conditions. In particular, a priori bounds are obtained. We also study a general multiple linear eigenvalue problem on a bounded domain.