On bounded entire solutions of semilinear elliptic equations
Copyright policy )On bounded entire solutions of semilinear elliptic equations
The author gives a result on the existence of infinitely many bounded entire solutions of the nonlinear problems \(-\Delta u+g(x)u^{\gamma}=0,\) \(-\Delta u+g(x)e^ u=0.\) Conditions assuring positivity are also given.
35B40, existence, bounded entire solutions, Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs, Nonlinear elliptic equations, 35J60, Second-order elliptic equations, supersolutions, General existence and uniqueness theorems (PDE), subsolutions, Stability in context of PDEs, second order semilinear elliptic equations
35B40, existence, bounded entire solutions, Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs, Nonlinear elliptic equations, 35J60, Second-order elliptic equations, supersolutions, General existence and uniqueness theorems (PDE), subsolutions, Stability in context of PDEs, second order semilinear elliptic equations
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