A concave-convex elliptic problem involving the fractional Laplacian

作者：Braendle, C.^*; Colorado, E.; de Pablo, A.; Sanchez, U.

来源：Proceedings of the Royal Society of Edinburgh: Section A Mathematics , 2013, 143(1): 39-71.

DOI：10.1017/S0308210511000175

• SOBOLEV TRACE INEQUALITY
• BOUNDARY-CONDITIONS
• POSITIVE SOLUTIONS
• INTEGRAL-EQUATION
• EXTENSION PROBLEM
• STABLE PROCESSES
• DERIVATIVES
• EXPONENTS
• CONSTANT
• OPERATOR

We study a nonlinear elliptic problem defined in a bounded domain involving fractional powers of the Laplacian operator together with a concave-convex term. We completely characterize the range of parameters for which solutions of the problem exist and prove a multiplicity result. We also prove an associated trace inequality and some Liouville-type results.

• 出版日期2013-2