Elliptic Equations with Critical Exponent
نویسنده
چکیده
where As3 is the Laplace-Beltrami operator on B' . Let 0* C (0, 7r) be the radius o r B ' , i.e., the geodesic distance of the North pole to OBq The values 0 < 0* < 7r/2 correspond to a spherical cap contained in the Northern hemisphere, 0* -7r/2 corresponds to B ~ being the Northern hemisphere and the values rr/2 < 0* < ~c correspond to a spherical cap which covers the Northern hemisphere. Finally, 0* = 7r corresponds to B ' = S 3 \ {South pole}. Our main focus is to identify the range of values of the parameters 0 * and A for which there exists a solution of Problem (1.1). Recall that a similar problem in R 3 has been investigated in [6]:
منابع مشابه
The Solvability of Concave-Convex Quasilinear Elliptic Systems Involving $p$-Laplacian and Critical Sobolev Exponent
In this work, we study the existence of non-trivial multiple solutions for a class of quasilinear elliptic systems equipped with concave-convex nonlinearities and critical growth terms in bounded domains. By using the variational method, especially Nehari manifold and Palais-Smale condition, we prove the existence and multiplicity results of positive solutions.
متن کاملNonhomogeneous Elliptic Equations with Decaying Cylindrical Potential and Critical Exponent
We prove the existence and multiplicity of solutions for a nonhomogeneous elliptic equation involving decaying cylindrical potential and critical exponent.
متن کاملSingular Elliptic Equations Involving a Concave Term and Critical Caffarelli-kohn-nirenberg Exponent with Sign-changing Weight Functions
In this article we establish the existence of at least two distinct solutions to singular elliptic equations involving a concave term and critical Caffarelli-Kohn-Nirenberg exponent with sign-changing weight functions.
متن کاملBuckling Analysis of Rectangular Functionally Graded Plates with an Elliptic Hole Under Thermal Loads
This paper presents thermal buckling analysis of rectangular functionally graded plates (FG plates) with an eccentrically located elliptic cutout. The plate governing equations derived by the first order shear deformation theory (FSDT) and finite element formulation is developed to analyze the plate behavior subjected to a uniform temperature rise across plate thickness. It is assumed that the ...
متن کاملCritical Exponents for Semilinear Equations of Mixed Elliptic-Hyperbolic and Degenerate Types
For semilinear Gellerstedt equations with Tricomi, Goursat, or Dirichlet boundary conditions, we prove Pohožaev-type identities and derive nonexistence results that exploit an invariance of the linear part with respect to certain nonhomogeneous dilations. A critical-exponent phenomenon of power type in the nonlinearity is exhibited in these mixed elliptic-hyperbolic or degenerate settings where...
متن کامل