Classification of Stable Solutions to a Fractional Singular Elliptic Equation with Weight
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DOI: 10.1007/s10440-020-00347-5
Abstract: Let $p>0$ and $(-\Delta )^{s}$ is the fractional Laplacian with $0< s2s$ and $h$ is a nonnegative, continuous function satisfying $h(x)\geq C|x|^{a}$ , $a\geq 0$ , when $|x|$ large. We prove the nonexistence of positive… read more here.
Keywords: solutions fractional; fractional singular; elliptic equation; equation weight ... See more keywords
Boundedness of stable solutions to nonlinear equations involving the p-Laplacian
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DOI: 10.1016/j.jmaa.2020.124122
Abstract: Abstract We consider stable solutions to the equation − Δ p u = f ( u ) in a smooth bounded domain Ω ⊂ R n for a C 1 nonlinearity f. Either in the… read more here.
Keywords: stable solutions; involving laplacian; nonlinear equations; solutions nonlinear ... See more keywords
ESTIMATES AND RIGIDITY FOR STABLE SOLUTIONS TO SOME NONLINEAR ELLIPTIC PROBLEMS
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DOI: 10.1017/s0004972720000702
Abstract: where Ω is a bounded domain, p ∈ (1,+∞) and f is a C nonlinearity. This equation is the nonlinear version of the widely studied semilinear elliptic equation −∆u = f (u) in a bounded… read more here.
Keywords: rigidity stable; stable solutions; elliptic problems; estimates rigidity ... See more keywords
On positive stable solutions to weighted quasilinear problems with negative exponent
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DOI: 10.1080/17476933.2017.1403429
Abstract: Abstract Let and , we prove the nonexistence of positive stable solutions of weighted quasilinear problem The result holds true for , or and , which is a positive critical exponent. Here and are nonnegative… read more here.
Keywords: solutions weighted; problems negative; weighted quasilinear; positive stable ... See more keywords
Nonexistence of stable solutions for quasilinear Schrödinger equation
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DOI: 10.1186/s13661-018-1087-7
Abstract: AbstractIn this paper, we study the nonexistence of stable solutions for the quasilinear Schrödinger equation 0.1−Δu−[Δ(1+u2)1/2]u2(1+u2)1/2=h(x)|u|q−1u,x∈RN,$$ -\Delta u- \bigl[\Delta\bigl(1+u^{2}\bigr)^{1/2} \bigr]\frac{ u}{2(1+u^{2})^{1/2}}=h(x) \vert u \vert ^{q-1}u,\quad x\in R^{N}, $$ where N≥3$N\ge3$, q≥5/2$q\ge5/2$ and the function h(x)$h(x)$… read more here.
Keywords: dinger equation; nonexistence stable; quasilinear schr; solutions quasilinear ... See more keywords