Positive solutions of critical quasilinear elliptic problems in general domains.
Positive solutions of critical semilinear elliptic equations on non-contractible planar domains
For semilinear elliptic equations of critical exponential growth we establish the existence of positive solutions to the Dirichlet problem on suitable non-contractible domains.
Positive solutions of elliptic equations in two-dimensional exterior domains.
Positive solutions of higher order quasilinear elliptic equations.
Positive solutions of inequality with -Laplacian in exterior 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.
Positive solutions of nonlinear elliptic equations in a half space in .
Positive solutions of nonlinear elliptic systems
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.
Positive solutions of quasilinear elliptic systems with strong dependence on the gradient.
Positive Solutions of Schrödinger Equations in Two-Dimensional Exterior Domains.
Positive solutions of semilinear elliptic problems in unbounded domains with unbounded boundary
Positive solutions of singular elliptic equations outside the unit disk.
Positive solutions of slightly supercritical elliptic equations in symmetric domains
Positive solutions of some coercive-anticoercive elliptic systems
Positive solutions of some nonlinear elliptic problems in unbounded domain.
Positive solutions of some quasi-linear elliptic problems
Positive solutions of the -Laplace Emden-Fowler equation in hollow thin symmetric domains
We study the existence of positive solutions for the -Laplace Emden-Fowler equation. Let and be closed subgroups of the orthogonal group such that . We denote the orbit of through by , i.e., . We prove that if for all and the first eigenvalue of the -Laplacian is large enough, then no invariant least energy solution is invariant. Here an invariant least energy solution means a solution which achieves the minimum of the Rayleigh quotient among all invariant functions. Therefore...
Positive solutions to quasilinear equations involving critical exponent on perturbed annular domains.
Positive solutions to superlinear second-order divergence type elliptic equations in cone-like domains
Positive unbounded solutions of second order quasilinear ordinary differential equations and their application to elliptic problems
In this paper we consider positive unbounded solutions of second order quasilinear ordinary differential equations. Our objective is to determine the asymptotic forms of unbounded solutions. An application to exterior Dirichlet problems is also given.
Positivity and anti-maximum principles for elliptic operators with mixed boundary conditions
We consider linear elliptic equations in bounded Lipschitz domains with mixed boundary conditions on . The main feature of this boundary value problem is the appearance of both in the equation and in the boundary condition. In general we make no assumption on the sign of the coefficient . We study positivity principles and anti-maximum principles. One of our main results states that if is somewhere negative, and then there exist two eigenvalues , such the positivity principle...